Steps to reproduce:
Not clear. Issue occurred with or without the compatibility mode.
Sites with WebSockets function do not work at all, the console shows "WebSocket connection to 'wss://some.url' failed: The operation couldn't be completed. (kNWErrorDomainPosIX error 57 - Socket is not connected)".
When the "Develop -> Experimental Features -> NSURLSession WebSocket" option is turned off, the issue is gone and WebSockets works seemingly with no problem. The option is on by default. Other users report that they have no problem with WebSockets with the option kept on by default.
Safari (Version 15.1 (176126.96.36.199.20)) on my system has the exact same behaviour on this issue.
This post described a similar issue, but suggested solution is to turn the option off, which is the opposite to my case.
Orion and macOS:
Orion Version 0.99.109-beta (WebKit 613.1.12)
macOS 12.0.1 (21A559)