private messaging doesn't work well without Uddeim

There is no private message system from Uddeim in Joomla 4. So the messaging system doesn't work well. When sending a mesage to another user, the user gets the message but there is no reply button to reply back to the user. Nor does the message tell you who sent the message. I guess without Uddeim, private messaging won't work well until someone picks up the ball and make the necessary effort to make it work with Joomla 4

Joomla's messaging system is not ment for private messaging.

Have you tried latest CB's internal one (enable "Private Message System" plugin with default Parameter Model: "Internal") ?