I have also been having this issue. I have been using Phone Link (and prev versions) for over 4 years.
The problem started in July, leading me to believe it was with an update. As mentioned above: the right 'Messages' pane will not update. I see new message notifications in the left pane, but I don't see them reflected in the right pane, no matter how much refreshing I do. Older messages are still in the right pane - but not any new ones. I am unable to view those message threads.
Of Note: I am able to send New Messages from this Pane - but any incoming history/thread is missing.
Its worth noting that other Tabs do still update - Pictures, Apps, etc - just not the Messages Tab. I have confirmed I can take a picture - and have it show up in the Photos Tab.
Also of Note: Certain Windows11 Desktop Notifications stop working with this failure.
For Example: you no longer get W11 Desktop Notification for New Message. Big issue for me; this breaks the recently released 'copy OTP text' functionality (for 2FA) that MS released as a feature (and it was quite handy when it worked).
Note: W11 Desktop Notifications for New Picture Taken have also stopped working commensurate with this issue. However, Desktop Notifications for New Email still work - which is strange. So the Bug seems to affect portions of the Phone Link Functionality (not all).
So far, I think it's a bug from a recent release and will need an update to fix.
I have reset Phone Link and re-added by Phone again. The first time it worked for ~week, then the same issue above re-occurred. I have just reset Phone Link for the 2nd time and will see how long this lasts.
UPDATE 8/7/2024 - The 2nd Reset on 7/31 has now stopped working again. ~1 week after resetting Phone Link and reconnecting Phone - the same Messages Pane Failure happens again. The failure is identical to the prior issue discussed above. So, something happens with the app a short time after you reset it - that causes the Message Pane to no longer work.
Also as above - certain WIN11 Desktop Notifications stop working again once this happens.
PC: MS Surface Pro 8 with the latest W11 23H2 Rel 22631.3958
Phone: Samsung S21FE with the latest One UI OS.
Phone Link: Ver 1.24071.86.0