Two US carriers are now rolling out One UI 3.1 updates to the Note 10 series

Well, in fact, it's the same update, it's just that it's for a different set of devices. Yes, Verizon is now rolling out the One UI 3.1 update to the Galaxy Note 10 and Note 10+ 5G users on its network (via Droid-life).
As expected, the update includes the March security patch, along with a plethora of new features and improvements added by Samsung, such as new Camera settings, app enhancements, as well as new Settings.
So, if you're on AT&T or Verizon networks and own either of the two Galaxy Note 10 series phone, you can check for the update by heading to Settings / About phone / Software updates / Check for Updates.