Okay, after talking with my senior advisor, unfortunately, you won't recover the Apple ID. If you were signed into the Apple ID section, you might be able to switch the security to two-factor, but since you're not and unable to get past the security questions, you're not going to be able to recover the Apple ID.
Here is what happened.
I only use the ***@me.com as a mail account since 2000 (updated, typo) to get access to Mail. Mail works fine on my MBP16. On my M1, I tried to add the same **@me.com to get access to mail on M1. I get the following screens sequence, regardless of whether I add an internet account or go to I forgot. This is what happened:
1 . Signing in the mail on M1
View attachment 1680704
2. Password accepted but locked out
View attachment 1680707
3. Birthday correct
View attachment 1680708
4. I forgot the spacing or capitals in one or more answersView attachment 1680709
I can use the locked out account on my MBP16, but as shown here, not on my M1. The question: why is my mail-identity working, but locked into an iCloud account security system?
All of you who want to send me friendly advise about password managers, 2FA etcetera, sure, but the main point is probably buried deep in this thread:
https://forums.macrumors.com/threads/apple-locked-me-out-and-says-thats-it.2271904/post-29316909