Re: EA Desktop not recognizing ownership of games also accessible through EA PLay.
Currently, I'm experiencing the exact same problem as you.
Ever since the launch of the EA desktop I've been gravitating towards the use of this app instead of Origins due to my own preference.
However, not long after the app no longer recognized that I owned a copy of the game I tried playing. In my case, that's Fifa 22.
EA Desktop, just like in the case stated by @Brass_Buckles, now claims that I need to log into my Microsoft account to verify my Game pass membership and thus EA Play.
I have never played Fifa with the use of any membership and already owned the game on Origins before ever playing it through the EA desktop.
This problem only occurs on the EA Desktop as the Origin launcher still recognizes my ownership of the game, it still allows me to update and launch Fifa 22 as it should since I own the game directly.
For me, it always shows the game but it simply won't allow me to launch or update the game without logging into my Microsoft account and verifying a membership I do NOT have.
Personally, I'm afraid to do so because I don't wish for the app to think that I'm not subscribed to EA Play and therefore will deny me access to the game altogether despite me owning it.
Due to this I've decided to also stick to Origins until this problem has been solved because I would lie if I said that isn't quite frustrating to deal with.
P.s. I have provided a screenshot to show the launcher recognizing that I own the game but still not allowing me to launch it.