I tried to migrate the private messages like you said on Joomla 4.2.7 with uddeIM 4.0 (dysfunctional) and CB 2.7.4. This partially works, messages are transferred, progress bar turns red, replies and read states not transferred.
I then reverted my setup back to Joomla 3.10.x with uddeIM 4.0 in a functional state, with the same CB 2.7.4. Then started the migration of private messages - this fully migrated all data!
For my production upgrade plan this means that the switch away from uddeIM must happen before the J4-upgrade step. I am posting it here in case someone stumbles over it and has the same problem.