iCloud Drive doesn't appear to work at all for me in the iOS 15.5 Simulator. As near as I can tell, it should. I've signed into my account in settings->Apple ID, iCloud, iTunes & App Store (and signed out/in several times). I've gone into iCloud settings and turned on/off/on/etc iCloud Drive and same for the app I'm developing. I've tried it on two different macs with the same results.
When I use the Files app on the Simulator, it shows 0 items, 33.13 GB available. The 0 is wron but the 33.13 TB available is right so it's getting some of the info from iCloud Drive.