Text message synchronization issue between iPhone 13 Pro and MacBook Pro (2019)

I have Text message Forwarding turned on at the Phone. If I read a message on the phone, it does not mark it as read on the Mac. If I delete a message on the phone, it does not delete it on the Mac. The reverse does not work as well. If I delete a message on the Mac, then click Delete on the Delete from all your devices popup, it does not delete the messages from the IPhone .

[Re-Titled by Moderator]