Having the project files stores pretty deep within the filesystem and using lenghty file names started to casue weird errors:

'no rule to make target'
'file not found' on .pro file

After a while (reinstalls of Qt etc.) I have discovered that the problem was indeed that the path to said files was too long. Including the file names it was over 150 characters long. I did not discover the exact limit nor whether it is somehow specific to my environment.

Shortening the path by renaming some of the directories to acronyms solved the issue.

I believe that the length of the path should not be an issue for qmake. Or if there is a reason for it then there could certainly be more informative error message as neither the error nor build output provided any hints whatsoever to what went wrong.