Why do movie playlists in the TV app not show up in the TV app on Apple TV?

I have just a few movies purchased in my TV app and wanted test playlists before buying more. However, the movie playlists I've created only show on the iMac version of the TV app.

When I go to the TV app on my Apple TV or even my PS5, I'm not seeing any playlists - I'm only seeing the default options on the left (Movies, TV Shows, Genres).

Am I misunderstanding how playlists function in the TV app? Why wouldn't they show across all devices?

Also, the fact I need to download the movie to my iMac before adding to a playlist is kind of a head scratcher - why is this required just to add to a playlist?

Minor annoyance, but wanted to see if I'm doing something wrong here.