Hi! You have done amazing work, and I'm ever grateful to your team for keeping AS3 alive!
I used sockets in some of my multiplayer games, but that's not where I ran into problems with Ruffle. Since those games only upgraded to sockets after an initial HTTPS connection, I haven't even gotten to the point of trying sockets yet. I mainly just used NetConnection.connect() for routine API calls, not to open a socket. AFAIK .connect() didn't open a socket, although I guess it had some two-way capabilities with Flash Media Server, but that's not how I used it. I just used it to initialize the NetConnection instance with the URI of a server endpoint that could receive AMF messages (usually translated on the backend with AMFPHP). I don't think it really left any sort of connection open. After that, you'd just make RESTful calls over that connection using netconnection.call(...args), and could send complex objects - even SQL result sets - back and forth without going through JSON or XML. But it was just a bunch of HTTP calls sending that data in Flash's own serialized format. You'd listen for NetStatusEvent or SecurityEvent to handle the results or errors. No sockets were involved. In conjunction with AMFPHP it was basically like a URLRequest without any structuring or destructuring needed to parse the results into AS3-friendly data types.
It would be amazing if only the RESTful kinds of NC connections and calls could work again through Ruffle, I think it might be all that's stopping my old games from running!
As a Ruffle developer who in my day job maintains some Flash-based websites, I'll note from experience that AMF serialization/deserialization in Ruffle has some definite issues, so that may be the issue for your games (the websites I maintain use https://metacpan.org/pod/AMF::Perl). See https://github.com/ruffle-rs/ruffle/issues?q=is:issue+state:....