Genmoji unavailable, Image Playground not working (MacBook Pro M1 2020, Sequoia 15.5, 8GB RAM)

I updated MacOS to the latest version available, and enabled Apple Intelligence. After a lot of fiddling to even download it (restarting the computer several times), Writing Tools works well in Pages, but Image Playground straight up doesn't work. I enabled the Photo Library, but no prompts seem to be processable.

Same thing with Genmoji: Character Viewer doesn't even have the menu for Genmoji. How come?