It's not great for direct chat, no. But it's good enough, and the "company file browser effect" really does carry a lot of weight. The actual chat module is easily among the weakest parts of Teams. The threaded chat in Teams workspaces functions well, but the UI design looks too much like normal chat (they're thankfully redesigning it) for something that isn't meant to be used the same way. It's more team workspaces + calls where the value is, IME.
Are you using it on linux ? Because I too experience the indicator that won't refresh, but only through ArchLinux/Firefox. No problem whatsoever on Windows 10.