You can. In the mobile app, click the “plus” button in the top left corner, and then “Manual activity”. On the website, it's the “Add manual entry” in the main menu. 

Still confused: can I get Strava somhow to display "Threadmill run" on manual or imported runs?

The easy way would be just to title the activity something like “Treadmill Run”.  Did you need it to show treadmill run for a different reason other than to make it obvious what it was when you view the activity?

Sorry, just saw your other post and I see what you are looking for.  If you want to add the treadmill tag to the activity, you will need to add it from the website version of Strava.  It isn’t available on the mobile app.

Sure, I do title it accordingly. I just don't understand why we have trailrun, MTB, gravelbike, but not treadmill nor peloton.

That would be the “Virtual ride” I think..?

There is a “virtual ride” and “virtual run” option when doing a manual entry on the mobile app, but those are more intended for things you do connected with other platforms like Zwift or Rouvy where you are riding or running in a virtual world.  ​@espelicht is looking for the “treadmill” tag which is currently only available on the web browser version of Strava and not available on the mobile app.

Virtual activities are with "fake GPS", mostly they are indoor. But not all indoor runs are virtual ones.