I got a new iPhone 8 and now I can't sign into my Apple ID?

Hi all. I purchased a new iPhone 8 through my wireless carrier tonight. It took a very long time because the tech seemed to be having a lot of issues - at one point he even had to get a different phone entirely and force the system to accept it's IMEI number. I didn't think much of it because I figured the store equipment was the problem. It signed into my iCloud backup because all of my photos are on it, so I figured everything was fine.

Now I'm home and I tried to use the App Store and it says "Can't connect to the App Store." I tried a hard restart. No luck.

I went to my settings, and it shows "iTunes and App Store > Off". If I try to select this, it first says "signing into Apple Media services" (or something like that) then says "authentication failure".

I've tried various "fixes". I tried signing out and signing back in again, but this appears to have made things worse, as now the phone won't sign back into my ID. It's in a purgatory, like half signed in (under "Settings" I have a "Sign Out" option, but in the App Store it doesn't consider me signed in).

I turned off my WiFi, which made the App Store stop saying "can't connect" but now if I try to download, it asks me to sign in to my Apple ID, and then doesn't accept it. It doesn't say it failed, or wrong password, it just doesn't download the app and goes back to the search page.

I tried resetting my Apple ID password.

I tried the Date and Time fix.

I feel like I've tried every normal fix, and none have worked - what gives, and how can I fix it?