I'm struggling to understand your use case here, but here are some thoughts that may be helpful.

You can use one Supabase Auth project to do all of your user management. You can use the JWTs issued by this project across any other system. You need to configure those systems to "trust" those JWTs, usually by sharing the signing key (JWT secret) with them. They can then base their allow / deny decisions on the JWT.

You can even do this with as many Supabase projects you want. You don't have to use Supabase Auth with all of them. Do note that once you use physically different machines, you need to sync them up and that's quite a big can of worms.