I have this same issue happen with New Teams immediately after switching to the New Teams from the Old teams. This is only on version 23272.2707.2453.769 of New Teams. Edit: After updating New Teams to 23285.3604.2469.4152, the issue disappeared.
Old Teams you could drag the Title bar successfully.
New Teams --> The user can't drag the Teams(New) window by clicking/holding on the Title Bar.
However,
The user can successfully use Win+right, Win+left, Win+down, Win+up to use the windows snap features.
The user can successfully double click on the Teams(New) window's Title Bar and it Restores/Maximizes the window.
Restarting the device does not fix the issue
Quitting and re-opening Teams (New) does not fix the issue.
Clearing Teams Cache and re-opening Teams (New) does not fix the issue.
I'm completely stumped as there are no settings in Teams to allow dragging from the Title bar.
Even worse, I am trying to report the Teams (New) version, but there is no About>"Version" in the Help/About sections of Teams(New). >>> Fine... *goes to Settings>Apps&Features>Teams(New)>* my version of (New) Teams is: 23272.2707.2453.769
Edit: I have submitted a Feedback Hub request (because that is where Microsoft actually does take care of things for me in the past, they would say, "We've got it. We got this feedback.") and the request for this issue is here: https://aka.ms/AAn55v7
Please help upvote this feedback if you have this same issue for it to gain traction in Feedback Hub. Thanks! Edit: Version 23285.3604.2469.4152 fixes this issue. After restarting the computer and/or waiting for Teams to update itself, the issue goes away.