After upgrading to Windows 11, you have Chat in the taskbar. This is really a Teams personal client, meaning that you end up with two Teams clients on the PC. To make life even more confusing, if you search Windows 11 for Teams, you see the personal version suggested first. Some pruning of clients is needed.
The Teams Windows and MacOS desktop clients will soon allow users to add a personal account to the set of Office 365 tenants they connect to. A great deal of excitement ensued after people saw Microsoft 365 roadmap item 68845 and assumed this meant that Teams would support connections with multiple work accounts. The ability to add more than one work account to your Teams profile isn’t available now as the update is to support connectivity to Teams at home (personal), but support for multiple work accounts is coming in the future.