Can't sign into iMessage on iPad

Saturday, May 27th, I was signed out of iMessage on my iPad overnight and I've been unable to sign back in since then. I changed my password that day thinking someone might've gotten access to my account somehow. I signed out of my Apple ID, signed back in, and shut off/turned back on my iPad, but nothing has helped.

I'll open iMessage and it'll prompt me to enter my ID/password, which I do, then it loads for a few minutes before giving me an "Unable to contact the FaceTime server" error. When I go into iMessage or FaceTime in settings, the entire app freezes and I have to close/reopen it to get it to work again. My OS is up to date and iMessage still works perfectly fine on my iPhone.

I have no clue why I was signed out to begin with (while I was fast asleep, mind you) and I'm at a loss for how to fix this. Any help is appreciated.