This isn't a verified solution, but if you still appear as "OfflineUser" after hitting "Let's Play" on the title screen try opening the Xbox Console Companion app and signing in there first.
I was having this issue as well, and it seemed that for whatever reason Microsoft wasn't registering my sign-in on the Xbox Gamepass app. However, launching Console Companion showed I was offline, and signing in there let me sign in when I launched Grounded as well.
Hope it helps!