So I've realized though Claude Desktop completely disabled all the models for me, Claude mobile app in the same account still has access to free models (I've noticed this just now because I rarely use Claude Mobile).

So, my first thought was that it's some sort of a cache invalidation issue. I restarted the app, didn't help. Logged out and logged back in, didn't help. But somehow it worked when I first logged out, restarted the app and then logged in. I guess that's the future we have to live in now.