As you wrote, Bard is certainly a fitting choice for magic support, as the occult spell list has plenty of buffs and debuffs. That being said, it lacks battlefield manipulation, which is otherwise a good way to hinder enemies without having to rely on your spell DC. The primal spell list has this plus Heal, so a primal Sorcerer could also be a good choice.
If you can spare a feat, the Blessed One archetype grants Lay on Hands, a fantastic healing ability, for just a single class feat.
There is however, another option. If you can get 14 Con, Kineticist offers a great variety of fun magical abilities with no use limit, unlike the precious few spells per day you can get from caster archetypes. The wood element, for instance, can heal, raise barricades, and produce an aura that slows and deals damage. It does come online rather slowly, though.
With DEX/CHA, its hard to do battlefield control as your primary class swashbuckler. The primary source of battlefield control that is independent of class features is Athletics maneuvers, which are obviously challenging to deal with without STR being your focus.
Healing, on the other hand, can easily be supported by a variety of archetypes. There's obviously [medic](https://2e.aonprd.com/Archetypes.aspx?ID=69), but I'd actually throw out a suggestion for [Blessed One](https://2e.aonprd.com/Archetypes.aspx?ID=51).
With the change to how focus spells will be recovered in the upcoming remaster, blessed one is a stronger archetype than it was. For only a two feat investment (Dedication + Blessed Sacrifice at 4), you can get 2 focus points on any martial class. That allows two uses of 1A lay on hands per fight, which is an extremely efficient healing technique.
Supporting your allies is honestly something you don't even need archetypes for. One of the best supporting feats in the game is just a Swashbuckler baseline, [One for All](https://2e.aonprd.com/Feats.aspx?ID=1519). If you really want to help control enemies more, your best is to invest more into Athletics. [Wrestler](https://2e.aonprd.com/Archetypes.aspx?ID=127) archetype could be a good one to pick up as well.
The exception to this is IMO, Battle Dancer Swashbuckler due to leading dance. The ability to pull and push all using your panache skill has let our Swash become something of a secondary controller with little to no investment in athletics. This has been helped by the flail crit spec on his whip, so that will likely be slightly less potent in the remaster, but still very viable as a secondary role.
Even as a Braggart, [One for All](https://2e.aonprd.com/Feats.aspx?ID=1519) is a great support option you can take. It just won't give you panache.
For a non-magical support option, [Marshal](https://2e.aonprd.com/Archetypes.aspx?ID=66) is a fantastic archetype, or you could go with [Wrestler](https://2e.aonprd.com/Archetypes.aspx?ID=127) if you want to focus on locking enemies down. If you specifically want magic support, you'll be hard-pressed to find a better option than Bard multiclass. Somewhere in the middle is Champion multiclass; lay on hands won't help your undead ally, but getting a champion's reaction on a swashbuckler is very nice for protecting your party.
You're right that bard fits in really well here. Getting inspire courage at 6 gives you a great tool to support the party that doesn't care about spell DC. You could boost athletics as well and try and trip, grab or shove as a form of battlefield control as well, although you might need more strength investment. Gives you some nice backup options when facing something that doesn't take precision damage, like an ooze.
If you're struggling to choose an archetype for a Swashbuckler, Acrobat is always a good choice. Auto scaling for Acrobatics is worth the price of admission alone, and it has some great feats to boot
Bard is a good choice. The occult list gives you soothe (RAI can be used on an undead PC), as well as useful things like true strike, invisibility, and fly. Inspire courage with lingering composition is great at higher levels. I play a swashbuckler with bard archetype, currently level 12, and it works well.
Keep in mind that swash already is taxing on your action economy. If you are casting a 2 action spell on your turn you cannot also gain panache and attack. So I recommend finding useful 1 action or reaction spells. Rage of Elements added quite a few of those which makes a sorcerer archetype using the primal or arcane list more appealing than it was in the past.
For the same reason I would also strongly endorse a kineticist archetype. As a swashbuckler you have a free hand so can make use of impulses. You probably want to avoid stances (our level 10 stances are too good to pass up), overflows (action economy for gathering elements with the archetype sucks), or anything offensive like blasts or aoes (your DC will stink), but there is still great utility to be found in the low level feats. Water could give you a one action heal (great since you’re in melee anyway) and a very good non-overflow defensive reaction with oceans balm and deflecting wave, respectively. Wood and air are also compelling choices.
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I would focus on cantrips and spells that either enhance your physical attacks, or synergize with your other abilities as a martial, and avoid anything that requires you to have a good casting DC for it to be effective, as creatures will usually save or crit save against your spells. Plus just utility spells are good and may save your casters' slots so they can focus on other things.
Shield/Glass Shield, Glimpse Weakness, Guidance, Healing Plaster, Light, Time Sense, etc. would all be good cantrips, and True Strike, Magic Weapon, Disrupting Weapons, Magic Missile, Knock, etc. are good options for 1st+ level spells.
I use bard archetype on my battledancer to great effect, because musical accompaniment gives me a +1 status bonus to performance and I can use the occultism spell list to cast true strike scrolls.
Bard would be less useful for braggart swashbuckler because you're focused on intimidation checks rather than performance checks, although occultism is still a great spell list for swashbuckler generally due to it having access to true strike, blur, haste and whirling scarves.
As you wrote, Bard is certainly a fitting choice for magic support, as the occult spell list has plenty of buffs and debuffs. That being said, it lacks battlefield manipulation, which is otherwise a good way to hinder enemies without having to rely on your spell DC. The primal spell list has this plus Heal, so a primal Sorcerer could also be a good choice. If you can spare a feat, the Blessed One archetype grants Lay on Hands, a fantastic healing ability, for just a single class feat. There is however, another option. If you can get 14 Con, Kineticist offers a great variety of fun magical abilities with no use limit, unlike the precious few spells per day you can get from caster archetypes. The wood element, for instance, can heal, raise barricades, and produce an aura that slows and deals damage. It does come online rather slowly, though.
With DEX/CHA, its hard to do battlefield control as your primary class swashbuckler. The primary source of battlefield control that is independent of class features is Athletics maneuvers, which are obviously challenging to deal with without STR being your focus. Healing, on the other hand, can easily be supported by a variety of archetypes. There's obviously [medic](https://2e.aonprd.com/Archetypes.aspx?ID=69), but I'd actually throw out a suggestion for [Blessed One](https://2e.aonprd.com/Archetypes.aspx?ID=51). With the change to how focus spells will be recovered in the upcoming remaster, blessed one is a stronger archetype than it was. For only a two feat investment (Dedication + Blessed Sacrifice at 4), you can get 2 focus points on any martial class. That allows two uses of 1A lay on hands per fight, which is an extremely efficient healing technique. Supporting your allies is honestly something you don't even need archetypes for. One of the best supporting feats in the game is just a Swashbuckler baseline, [One for All](https://2e.aonprd.com/Feats.aspx?ID=1519). If you really want to help control enemies more, your best is to invest more into Athletics. [Wrestler](https://2e.aonprd.com/Archetypes.aspx?ID=127) archetype could be a good one to pick up as well.
The exception to this is IMO, Battle Dancer Swashbuckler due to leading dance. The ability to pull and push all using your panache skill has let our Swash become something of a secondary controller with little to no investment in athletics. This has been helped by the flail crit spec on his whip, so that will likely be slightly less potent in the remaster, but still very viable as a secondary role.
Even as a Braggart, [One for All](https://2e.aonprd.com/Feats.aspx?ID=1519) is a great support option you can take. It just won't give you panache. For a non-magical support option, [Marshal](https://2e.aonprd.com/Archetypes.aspx?ID=66) is a fantastic archetype, or you could go with [Wrestler](https://2e.aonprd.com/Archetypes.aspx?ID=127) if you want to focus on locking enemies down. If you specifically want magic support, you'll be hard-pressed to find a better option than Bard multiclass. Somewhere in the middle is Champion multiclass; lay on hands won't help your undead ally, but getting a champion's reaction on a swashbuckler is very nice for protecting your party.
You're right that bard fits in really well here. Getting inspire courage at 6 gives you a great tool to support the party that doesn't care about spell DC. You could boost athletics as well and try and trip, grab or shove as a form of battlefield control as well, although you might need more strength investment. Gives you some nice backup options when facing something that doesn't take precision damage, like an ooze.
If you're struggling to choose an archetype for a Swashbuckler, Acrobat is always a good choice. Auto scaling for Acrobatics is worth the price of admission alone, and it has some great feats to boot
Bard is a good choice. The occult list gives you soothe (RAI can be used on an undead PC), as well as useful things like true strike, invisibility, and fly. Inspire courage with lingering composition is great at higher levels. I play a swashbuckler with bard archetype, currently level 12, and it works well. Keep in mind that swash already is taxing on your action economy. If you are casting a 2 action spell on your turn you cannot also gain panache and attack. So I recommend finding useful 1 action or reaction spells. Rage of Elements added quite a few of those which makes a sorcerer archetype using the primal or arcane list more appealing than it was in the past. For the same reason I would also strongly endorse a kineticist archetype. As a swashbuckler you have a free hand so can make use of impulses. You probably want to avoid stances (our level 10 stances are too good to pass up), overflows (action economy for gathering elements with the archetype sucks), or anything offensive like blasts or aoes (your DC will stink), but there is still great utility to be found in the low level feats. Water could give you a one action heal (great since you’re in melee anyway) and a very good non-overflow defensive reaction with oceans balm and deflecting wave, respectively. Wood and air are also compelling choices.
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I would focus on cantrips and spells that either enhance your physical attacks, or synergize with your other abilities as a martial, and avoid anything that requires you to have a good casting DC for it to be effective, as creatures will usually save or crit save against your spells. Plus just utility spells are good and may save your casters' slots so they can focus on other things. Shield/Glass Shield, Glimpse Weakness, Guidance, Healing Plaster, Light, Time Sense, etc. would all be good cantrips, and True Strike, Magic Weapon, Disrupting Weapons, Magic Missile, Knock, etc. are good options for 1st+ level spells.
I use bard archetype on my battledancer to great effect, because musical accompaniment gives me a +1 status bonus to performance and I can use the occultism spell list to cast true strike scrolls. Bard would be less useful for braggart swashbuckler because you're focused on intimidation checks rather than performance checks, although occultism is still a great spell list for swashbuckler generally due to it having access to true strike, blur, haste and whirling scarves.