@Steinsplitter says this occurs both when logged in / out.

Confirmed. Seems to be limited only to File pages (my test Mainspace page is fine)

My hunch is that this has nothing to do with varnish itself, since it happens both when logged in / out.

And the database itself sesems to be fine, at least the page / image / filearchive tables. (https://test.wikipedia.org/wiki/File:Test_Image_2.jpeg for test image, please do not purge atm)

(am fairly unfamiliar with our LocalFile setup, am trying to trace the actions caused by action=purge, to see what might fix this)

Side note: the less obvious but much easier way to upload screenshots is to just drag&drop the file into the comment box. That will create a file, not a mock - both easier to do and is displayed more nicely.