This known bug should have been fixed in Version 25.0.0 (ID 1401). The bug is still present in the current version (26.1.0).
I'd like the content of the Projector window to be updated when a different scene is selected. Is there a workaround for this?
Projectors can be set up from many different locations in OBS. Where the projectors are setup will influence the way they work.
If you hover over the Preview window (in studio mode) and apply your projector from their I think you will get what you want.