It's confusing having that section at the top of a tutorial titled change the user name, as it specifies but doesn't change anything.
And it will soon be unnecessary anyway:
I read the thread and couldn't see how it answered the question either.
OP is using Microsoft Authenticator on an Android phone.
The two links you've provided so far are about using different apps on Windows.
You could be right, but I worked for a company with 150,000 employees which insisted that every laptop had a pre-boot Bitlocker PIN.
They were told that if they forgot it, their laptop would be wiped and restored to defaults as it wasn't known by anyone else.
If you click "Save to your Microsoft account" and refresh the page at https://aka.ms/myrecoverykey it should appear with today's date.
I just tested this with mine and a current recovery key got added for a second time with the new date.
Why do you assume that key is not your current recovery key? (I have current recovery keys in my Microsoft account from 2018/2024.)
No, deleting old recovery keys will not cause a new one to be saved or displayed.