Same issue here for multiple random users. The only workaround is to sign out and sign back in, that lasts a few days before disconnecting people from Teams again. It started in the last few months.
I've seen a couple of times a banner message along the lines "Please wait while we retrieve your messages"
It never retrieves anything.
Clearing cache, Resetting app, Reinstalling app does absolutely nothing to help this issue.
User gets disconnected, they sometimes able to receive messages, but any that are sent by that user get stuck on the client side.
Not related to group chats - can't send messages to anyone in any of the channels.
It is not a network issue, people on different networks, on VPN and off VPN get this.
Admin won't be able to help you with anything - Otherwise there would be more troubleshooting suggestions other than usual clear "cache", "restart app", "log out, log in".
I don't think MS ever comprehends how frustrating it is for a business to lose sales, clients and orders, just cause your messages didn't send. Why should we not move to another supplier for cheaper, better version of this mess, that MS keeps peddling?