Multifactor authentication issue has completely broken my account

You seem to be doing all the right things (I don't know that the somewhat generic information provided in earlier posts really tells you anything you haven't already outlined in your posts). In particular when you get a message where Apple says an error is unavailable or unknown, I would contact Apple about this: This support article has various country telephone numbers for contacting Apple for support and service ➔ Contact Apple Support - Apple Support For some countries look under “Other” listing at the end of each region. Not every country has telephone support.

An active internet connection is required for 2FA verification, authentication, and accessing your Apple ID account.

Connecting to Wi-Fi doesn't necessarily mean you're connected to the internet.  --> Internet not available, WiFi and Cellular … - Apple Community

On iOS devices, you may sometimes see that you're connected to a Wi-Fi network, yet experience no actual internet access. This can be confusing, especially when both Wi-Fi and cellular signals are showing, but nothing loads.

Here’s what’s happening:

1. Wi-Fi without internet: Your iPhone or iPad may connect to a Wi-Fi network (like a router or hotspot), but if that network doesn’t have a working internet connection — due to ISP issues, router problems, or restricted access — you won’t be able to browse or use online services.
2. "No Internet Connection" warning: iOS tries to detect this. If it finds that the Wi-Fi you're connected to has no access to the internet, you'll see a message like “No Internet Connection” under the Wi-Fi name in Settings.
3. Why iOS doesn't always switch to cellular: If you’re also on a mobile data plan, your iPhone should switch to cellular if the Wi-Fi is unresponsive. However, iOS doesn’t always do this automatically. There are two features that affect this:
   1. Wi-Fi Assist (Settings > Cellular > Wi-Fi Assist): This allows cellular data to take over when Wi-Fi is weak, but it may not trigger if the Wi-Fi is technically “connected” but just not working.
   2. Low Data Mode or VPNs can prevent automatic switching.
4. Troubleshooting tip: If you’re connected to Wi-Fi and suspect a lack of internet, try:
   1. Opening Safari and visiting a reliable website (e.g., apple.com).
   2. Turning Wi-Fi off and back on.
   3. Forgetting the network and reconnecting.
   4. Switching to cellular manually if it’s available and working.

Apple account has 2FA and not Multi-FA as described by you.

On your iPhone or iPad: go to Settings > [your name] > Sign-In & Security. Tap Turn On Two-Factor Authentication. Then tap Continue and follow the onscreen ...

Two-factor authentication for Apple Account