Also having this issue on Mac, but I found a possible cause and solution without having to exit / restart. My suspicion is Teams is getting confused about what is selected and trying to navigate the UI, rather than the text.
Cause:
This seemed to start happening immediately after I finished editing my last message having pressed the "up" cursor to edit it. On completion, I wasn't able to move left and right.
Fix:
From having the text entry box select, I hit tab to switch to selecting from the format panel. I then used the left and right cursors to change my selection a couple of times. Finally, I hit "Shift+Tab" to return to the text entry box. I was immediately able to use left and right to move through text again.
Solution (until MS fixes the problem):
Ensure you are typing in the text entry box. Press tab. Press right. Press left. Press Shift+Tab.
Edit: I had an issue earlier today where everything except CMD+A (ctrl+a) was working for me in Teams, which was fixed by tabbing and shift-tabbing a few times until getting back to the text box, which also fixed it. I don't know why this is working but it seems Teams gets confused as to where certain commands are taking place, and you can force it to bring it back to the text box by cycling through where I assume it's been locked to in the UI.