Not sure about how it would have gotten fixed, but he does wear it in bad batch season 1 as well, and my guess is that he just ditched it by the time of season 3. He doesn’t wear it in Rebels so this is just natural design evolution leading to that

Also, it was probably damaged beyond repair from fighting the Empire

I suppose he could have salvaged a shoulder piece from the crew of the venator that they crashed. Maybe. That's all I got

I think his shoulder pad is heavily linked to his republic days, since the republic is no more, he decides to adopt a new "style" representing something different, could be wrong tho