I'm having the same issue as well. I've tried both personal and business emails and cannot for the life of me get a testflight invitation for even myself. I have other apps on testflight that I can get new build updates just fine. It's just establishing new testers seems to be an issue

I subscribed to this thread and got an email notification for this, just seems that TestFlight has took a holiday. Come on Apple, we all need you to fix this!