I've had this issue for about 2 weeks now and have spent about 3 hours on the phone with Apple support during the past week or so. It seems to be an intermittent issue that can sometimes go a day without issue then occur on pretty much every new message the next day.
I've currently got a support case open with Apple's 2nd line support but unfortunately it's not really progressed much. For me, the issue exists with both Firefox and Edge Chromium and have tried disabling adblockers, clearing cookies and data, private mode as well as using my iPhone's hotspot mobile connection, none of which made any difference. In my most recent conversation with Apple support a couple of days ago they seemed to think it was a DNS server issue, but I've tried Cloudflare, Virginmedia and Google DNS servers all to no avail either.
The intermittent, non-repeatable nature and the coincidental timing of people having the same problem would, to me, suggest that this isn't a client-side issue so I'd be interested to know if anyone has seen the problem resolved for longer than a few days.