I switched from Gitea to Forgejo when Forgejo was announced, and it was as simple as changing the binary/docker image. It remains that simple today, and will remain that simple for the foreseeable future, because Forgejo cherry picks most of the changes in Gitea on a weekly basis. Until the codebases diverge, that will remain the case, and Forgejo will remain a drop-in replacement until such time comes that we decide not to pick a feature or change. If you're not reliant on said feature, it's still a drop-in replacement. (So far, we have a few things that are implemented differently in Forgejo, but still in a compatible way).
Let me offer a few reasons to switch:
Forgejo - as of today, and for the foreseeable future - includes everything in Gitea, but with more tests, and more features on top. A few features Forgejo has that Gitea does not:
Forgejo makes it possible to have any signed in user edit Wikis (like GitHub), Gitea restricts it to collaborators only. (Forgejo defaults to that too, but the default can be changed). Mind you, this is not in a Forgejo release yet, it will be coming in the next release probably in April.
Gitea has support for showing an Action status badge. Forgejo has badges for action statuses, stars, forks, issues, pull requests.
...there are numerous other features being developed for Forgejo that will not make it into Gitea unless they cherry pick it (they don't do that), or reimplement it (wasting a lot of time, and potentially introducing bugs).
Forgejo puts a lot of effort into testing. Every feature developed for Forgejo needs to have a reasonable amount of tests. Most of the things we cherry pick for Gitea, we write tests for if they don't have any (we write plenty of tests for stuff originating from Gitea).
Forgejo is developed in the open, using free tools: we use Forgejo to host the code, issues and releases, Forgejo Actions for CI, and Weblate for translations. Gitea uses GitHub to host the code, issues and releases, uses GitHub CI, and CrowdIn for translations (all of them proprietary platforms).
Forgejo accepts contributions without requiring copyright assignment, Gitea does not.
Forgejo routinely cherry picks from Gitea, Gitea does not cherry pick from Forgejo (they do tend to reimplement things we've done, though, a huge waste of time if you ask me).
Forgejo isn't going anywhere anytime soon, see the sustainability repo. There are people committed to working on it, there are people paid to work on it, and there's a fairly healthy community around it already.