2-factor authorization failed me

Slap:

I've read -- and re-read -- your post several times last night and this AM

I can certainly sense - and understand - your frustration.

I'm confident that you'll get all of your accounts squared-up in due time.

I "suspect" -- but absolutely do NOT "know" -- that you encountered pieces of the "old / legacy" verification scheme rather than the new.

Beyond that, all anyone can do going-forward is to better understand Apple's 2FA. With that in mind:

A very good explanation of the 2FA concepts, and user steps is available here:

https://support.apple.com/en-us/HT204915

If reasonably well understood, you shouldn't encounter any real problems using 2FA going-forward.

That said, IMHO a few points from the document deserve a little extra emphasis:

1) Commit your AppleID and chosen password to absolute rock-solid memory.

Be able to accurately regurgitate them at unexpected times and while under stress.

You rarely need them, but when you do, you often REALLY need them.

(Example: Using FindMe to locate and/or restrict use of your misplaced / stolen mobile device.)

Keep the password VERY secure (i.e. only in your brain). With an AppleID and password, any ne'r-do-well can disable your devices.

(2FA codes are not required for this function)

2) Use multiple "trusted phone numbers"

Think-ahead about how you'll receive your codes if any one of your devices -- or catastrophically all at once -- are lost or inaccessible.

2) Keep your "trusted phone numbers" up-to-date.

While this might seem blindingly obvious; like any other "housekeeping task" it's easy to let it slide and end up w/ your codes being sent to no-longer-used phone number(s).

3) Practice, practice, practice.

The first time to use FindMe is NOT when you've really lost your device.

Give it a try, beforehand. For example:

Actually "mark" your mobile device as "Lost."

Actually set the screen message with a "If you find this phone call ... " message.

Actually "find" your phone and place it back into normal operation.

Use all of your trusted phone numbers to receive codes.

Finally, if you don't do all of this, Apple still provides good mechanisms to recover.

However these methods - by their nature - require extra steps, time, and mental resources from you; and they almost always need to occur at times of already elevated stress.

Cheers.