Synchronize with Apple TV app

So, in the new versions of MacOS (Catalina and later) iTunes has disappeared. The music is now in the Music app, the movies have moved to the Apple TV app.

But. Maybe I don't get it right, but I am a bit disappointed about this.

On my Mac MIni M1, there's no problem. My home movies I edited in FC Pro, have moved to the Apple TV app indeed.

But if I hoped (which I did indeed) that I could also watch these home videos on my MacBook Air (also Mac OS Big Sur), I found out the hard way that this is not the case. The library is empty…

Of course I would also like to see them on my TV set, using my Apple TV 4K.

Am I right: isn't it possible to sync my home made movies between these three devices? This is just too bad…

Or is it possible? If so, can you please tell me how?