Huh, Safari has the same issue. Guess it's some deeper or configuration issue. Please feel free to close this issue! If I can diagnose the issue, I'll post a reply in case anyone else encounters the same thing.
Update: based on this StackOverflow answer, I disabled
Develop > Experimental Features > NSURLSession WebSocket and now Discord WS works. Based on this bug report, it seems that the
NSURLSession WebSocket feature is enabled by default (by WebKit itself?) on macOS Monterey but is buggy with respect to compression. Neat!