Microsoft Teams may sometimes need more time to handle chat messages.
When such issues occur, the service may take longer than expected to deliver new chat messages.
ensure this is not a internet problem.
power cycle your modem if necessary.
Or use a different web link such as a mobile hotspot.
sign off and reboot your equipment
Try performing a full logout followed by a full login.
This will reset your connection to the Microsoft Teams servers.
Sign out of your Teams account and reboot your setup.
Then log back in and test whether the chat area is fully functional.
Try a Different Teams Version
The chat problem usually affects computer users.
flush the Cache
Clearing the cache solved this issue for many users.
Speaking of clearing the cache, run Disk Cleanup as well.
In other words, double-check to clear all your temporary Internet files.
After you did all that, cycle your rig.
Launch Teams again and test whether the chat messaging issue has been solved.
Reinstall Teams
Well, if the problem persists, try uninstalling your Teams app.
Let us know if you managed to fix the chat.