Microsoft appear to be working on a brand-new Teams app, and is a Progressive Web App (PWA).

The new desktop app is based on Microsoft Edge so runs in the browser without all the Edge noise around it, such as the menus, address bar, etc.
At the moment, the app doesn’t work as it isn’t enabled yet however hopefully we’ll see this change quite soon.

The new Teams app is marked as Alpha so when and if it starts working, there may be bugs, crashes and other inconsistiences.
Download the Teams Alpha app here.
[UPDATE – 5th March 2021 17:46]
Microsoft seem to have taken the download offline.