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github runs ms flavor of git web, while codeberg runs a fork of sorts of forgejo wich is fork of gitea.
You also forgot gitlab. bit bucket? I dont trust my personal code with any of these.
You can host gitea, forgejo, gitlab (as far as i have tested), not sure about bit bucket.
Github has many things i dont use, like CI/CD, Gitlab has them also and follows kinda close to github, you can if you want, really customize all of your actions etc. While i dont use these, and just push my commits, it dont matter wich one to use.
Ofc there are terms of service so depending on what you use your milage may vary.
Imo, self host is the only way. If you want to publish the code then gitlab, or if you dont mind the old bill snooping around with his AI eye then github.
Forgot to mention, compared to gitlab (selfhosting) gitea/forgejo uses like very very little resources. I ran gitlab for half a year, but it used too much of my ram and cpu, so then i found gitea, wich ran like only on 100mb ram and practically idle, then i found out that gitea sold out to corpos, and will have the same fate as other so called open source projects that turned into for profit projects, so people rallied up and forked it into forgejo. So i moved to forgejo (selfhost) - same repos from gitlab -> gitea -> forgejo. So far no problems
Also if youre shady then you can host some "hot" code on https://git.hackliberty.org/explore/repos - they run same gitea