Xbox Game Pass Ultimate x EA Play

So, I've activated a trial for XGP Ultimate and have it up and working on my Microsoft account. I wanted to test out the EA Play functionality, so here's what I did:

1. Sign in to the Xbox App on Windows 10 and to the EA Desktop app (the new origin thing)

2. In the Xbox app, find and select an EA Play game (in my case the original PvZ) and click on Install.

3. A "Link accounts" dialogue pops up from EA Desktop, I accept it to link MS with Origin. (If I go to my EA Account page, I can see my Xbox profile is properly linked)

4. Nothing happens, so I click Install again in Xbox, now that my accounts are linked.

5. EA Desktop shows the PvZ product page, with options to subscribe to EA Play for money or to buy the game standalone.

XGP Ultimate should include EA Play without any extra fees, so what am I missing?

Quick update: After posting this, I clicked on the arrow next to my avatar in EA Desktop, then on My profile and it shows "Play" next to my Origin name, so I guess I have EA Play, but also don't have it at the same time, since I can't download anything from it?