I would add to that -- in the previous setup, we got that red asterisk when we had a new chat message, just like the asterisks for conditional moves, notes, etc. Now you have to specifically open the chat to see if perhaps you have a new message. I'm talking about daily games here on the desktop version. Thanks!
Chat and message notifications

It’s well over a year since the last comment but it’s still an issue. I don’t see a chat comment unless I go into the game. It would be great to have a settings option to choose to have a notification via mobile or email to say a chat message has been left. Or am I missing something??

The android app notifies me when my opponent moves. Why not when he chats? No clue how long I've ignored them without timestamps either. Oof
Dear Chess.com, can you improve the functionality of chat messaging feature within a chess match. The chat feature with the two speech bubbles icon.
Just some of my issues:
1) No date and time stamp of when a chess chat message was sent or received by an opponent.
2) No email notification of a chess chat message sent by an opponent.
3) No indication or icon counter on the dashboard or within a chess match of new/unread chat messages.
Thanks.