question

The behavior works for me. Sometimes if I am setting the group tag in the portal, i need to change it a few times for it to update, then wait 15 min or so for it to update. After I change the group tag from the old group tag, it gets added to the other AAD group and then has the new appropriate Autopilot profile assigned. Have you tested it in PowerShell to see if it works better for you?

Eg:
Connect-MSGraph
Set-AutopilotDevice -id <ID> -groupTag <GroupTag>

Or even use PowerShell to see if it has set the new group tag or if it shows the old group tag just by using "Get-AutopilotDevice"

Is it possible that the device hasn't had time to sync. Generally speaking, Intune uses different refresh cycles to check for updates to configuration profiles. If the device recently enrolled, the check-in runs more frequently. For Windows 10 device, it will sync every 3 minutes for 15 minutes, then every 15 minutes for 2 hours, and then around every 8 hours. You can also open the Company Portal app, Settings > Sync to immediately check for policy or profile updates.

Yea I waited quite awhile changing it manually in the portal. The same issue happens with other devices as well. I went into powershell and configured grouptag there, and it's doing some sort of strange stuck state -

deploymentProfileAssignmentStatus : assignedUnkownSyncState
deploymentProfileAssignmentDetailedStatus : none
deploymentProfileAssignedDateTime : 9/24/2020 8:34:08 AM

That assigned date is from yesterday while I updated group tag ~30 mins ago. I know with dynamic groups it can take a bit. I'll let it sit a bit longer and report back.