It appears to be 30 per domain, not “hundreds”, at least as of the time this answer was written. I didn’t see anything more recent that contradicted this.

In practice, this is unlikely to be problematic unless you’re using multiple websockets per page, but the limit of 6 TCP connections is even less likely to be a problem if you’re using HTTP/2, since those will be shared across tabs, which isn’t the case for the dedicated connection used for each websocket.