What is the version number of your Teams application?
I have just updated Teams app on another computer with another Teams account. The version number of this update is 26005.213.4315.4117. The Download feature works on this update too, but there is some peculiarity with the Settings -> Files and links page.
The labels on this page are just place holders, but the buttons work. This often happens after a new update, but the issue is usually resolved after restarting the app. However, this was not the case with this update.
If there is an issue with your particular update, then I would suggest joining the "Insider" program.
After joining the Insider program, the application should be updated to this latest Insider version, which I'm currently using on my Windows computer.