What are your thoughts about the wger project [0]? It is a FLOSS AGPL-licensed self-hosted fitness/workout/nutrition manager that has existed for almost a decade (I think?) It's a django app and has a companion flutter app that runs on android/ios/windows/linux/macos. It supports multiple users and could even be used to run a gym. Body.build [1] is a newer FLOSS project (also browser-based) that is focused around building a weight lifting program. The author of body.build also contributes to wger.
I'm using wger in my homelab and while there are a lot of moving pieces to the self-host process, it works well. I'd say the biggest limitation is the comprehensiveness of their exercise database, but that is something that many people have recognized and are steadily expanding. If anyone is willing to contribute exercises (and exercise media) to this AGPL licensed project, they would definitely appreciate it!