Well, in the end: it became a (soft) fork. In the FAQ, an answer is that Forgejo being similar to LineageOS and Android's connection towards each other. Or how QT Company & KDE Free QT Foundaion are releated to one another.
For now, looks like Codeberg will be replacing Gitea with Forgejo codeberg/gitea from v1.18
Yes, it's also capable for realtime collaboration. HedgeDoc just joined the Fosstodon instance on Mastodon at November, while Etherpad has a bot on it with 0 news.