I think it would make a lot of sense for Edgeworth to start wearing his bagde by the end of aai2.

This is more of a headcanon, but I think like after he regained his badge by the end of that case, wearing the badge, at least for trials, would be like a symbol that he finally became proud of being a prosecutor, that he finally found his own path. That is kind of the whole deal with aai2 tbh, Miles pursuing the truth and finding his own place. Something he genuinely wants to do.

It also would symbolize his growth, that he is now a different person, no longer the demon prosecutor of years ago, since, technically, the one who taught him to leave his badge in his pocket was von Karma.

Sebastian, on the other hand, would start hiding it. After the whole ordeal with Blaise and being slapped in the face countless times, he'd probably start to feel 'unworthy' of using the badge, and would take it off, only putting back on again when he deems right, when he leaves the person Blaise made him out to be in the dust.