I only tested on Firefox 94.0 and Chromium 96.0.4664.45 on Linux (Ubuntu). I guess it’s possible that Chrome is different than Chromium in this regard, but I’d be surprised. I didn’t test Edge.
If you follow some of the discussion in the issue I filed (linked above), you’ll see some chatter on the Firefox bug tracker about similar issues. So I do think this is down to how the browser interprets the content headers. The question for us is whether we look to the browsers for a solution or consider a workaround for this specific case.