The TL;DR; is that it allowed Gitea to better work with companies that wanted to fund them but couldn't fund individuals directly, moved the Gitea trademark to an entity that could outlive the creator, etc.
There hasn't been any significant changes to how Gitea operates or can be used from a user point-of-view since the change happened.
Forgejo is a fork of Gitea that will pull changes made from Gitea, without being a company. In the events that Gitea goes to shit, it'll be there as a replacement.
I do not think there is a consensus.
Personally, I am not moving anytime soon. IMO so far gitea has not done anything wrong yet (they just put them in a position where is easier for them to do it, eventually). It is still a good thing forgejo exists... but I can't stand the name, heh (also, I like the green theme of gitea :P).
Personally I am conflicted. On one side gitea switching to a for-profit is worrying, even if they didnt do anything wrong yet. I like codeberg (non-profit behind Forgejo), but I also want to support devs actually working on the product. So I think for now I'll stay with gitea, but I won't hesitate to migrate to Forgejo if they start to act stupid
I switched to Fogejo just by swapping out the image. So far gitea hasn't been malicious with its trademarks now being owned by a private company, but I feel better using software that is more closely tied to a nonprofit. I see no reason to switch back.
Probably switching container from gitea to forgejo will just work… I recently switched my deployment, "issues" I had with postgres, but it was related to updates on helm-chart part (gitea upgraded postgres as well, so either update or switch made me same work to do).