> I don't think their proxy server would use Opera Mini as the user-agent.
It does, I just checked:
> Opera/9.80 (Android; Opera Mini/87.0.2254/191.361; U; en) Presto/2.12.423 Version/12.16
> What I seem to remember, was that they run this proxy which did the fetching for you, did some ridiculous compression or similar, and then sent you the compressed reply.
That's Opera Turbo, a feature of Opera Mobile (which is a full browser, HTML, JavaScript and all), which indeed compressed images and other media in a lossy way (and text losslessly, if it wasn't already at the HTTP level, I assume).
Opera Mini actually renders HTML (and executes JavaScript for a couple of seconds) server-side and then sends a binary version of that pre-render to the phone. I imagine it to be closer to SVG or PDF than to HTML and CSS.