Wondering whether this could be a breaking change for some setups - (for whatever reason) checking for text/plain on error responses but now getting HTML.

I don‘t think so. We previously had HTTP 404 already, so that would have been much more reliable to check for. But to be honest, I don‘t see many use-cases where you would need to check the response anyway (as the media URLs are mainly used for linking to files). Do you have an example use-case?

Having looked at it again, you're right: I think it's a good change that won't really cause issues anywhere.

Questions is if this is urgent or could wait until 3.6.0 since strictly it's a breaking change (public method returns something different now) - one that won't break many (if any) actual setups though.

You are right, it's probably better to move this to 3.6.0.

Marking it as draft to avoid that we merge it by accident. The code is already done.