This problem just started for me. It wasn't happening earlier today. When I switch to an active chat session with someone, I see the thin black scroll bar appear on the right side of the window. Then it vanishes, and no amount of cursor positioning will cause it to reappear.
Editorial: The whole idea of super-thin, disappearing scroll bars never made sense. People need to scroll. Traveling laptop users (like me right now) don't have mouse wheels. We need robust, visible, "grabable" handles for scrolling and for resizing windows. It wastes my time whenever I'm trying to position the cursor just right on some narrow scroll bar, or trying to get just the right pixel position to resize a window.
Back to the missing vertical scroll bar in New Teams: I rebooted my laptop, I closed and restarted Teams from the system tray, and I still have no scroll bar for scrolling vertically to see the history in a chat session. If I click on the latest chat, then use the up-arrow key to scroll up through the chat history, the little thin scroll bar will briefly appear on the right side of the window. But it vanishes when I try to catch it with the mouse cursor. This is a very real and rather glaring bug.
I'm running Windows 11 on a Lenovo T490.