I made a test page of my game and I downloaded and installed the free demo on the app. Once the demo was installed, I downloaded the paid version (using a key I generated), except the Itch app didn't install it. I can't switch from the demo version to the paid version either when I go to my library in the app.

How do I get the to switch? I want the transition from demo to paid version to go smoothly for my players.

Same here.

I have a game configured like this:
- an embedded demo, 
- a downloadable  demo
- a paid full version
The app will only install the embedded version, even if you registered the full game.

And another one:
- an embedded demo, 
- a paid full version
The app doesn't show any install button, only "buy"...

That doesn't make much sense. I'm pretty sure the app used to let you choose which file to install. If that choice is gone, the app should check the paid version first, then a free demo, and only then the embedded version...