EDIT: It's using EventSource. If you open the debugger and Cmd+Shift+F for `onmessage`, you'll find where it receives the message, and you can add a breakpoint, which you can then right click and change to a logpoint, to log the contents of the message. There is probably a one-liner you could paste into devtools to do some prototype hacking of window.EventSource, but I don't have time to figure that out atm, and can't find anything in a few quick searches of GitHub code.
EDIT EDIT: Just tried Safari, it does indeed show up as a spinner, but I still can't see the actual messages in DevTools.
[0] https://github.com/Yaffle/EventSource/issues/79
[1] https://bugs.chromium.org/p/chromium/issues/detail?id=102589...