I'm just here to say that I seem to have resolved the issue on my end. For those who already know what the problem is, this might not help but for me I was literally barking up the wrong tree in my trouble shooting.
The long and short of it is that I had already linked my xbox gamertag to EA, likely years ago and I've since forgotten about this and have been using a different EA account since. The error message is not indicative of what is happening. The problem was that my gamertag already had a linked EA account and when I used account recovery I was recovering a new/different account because I had completely forgotten about the old one.
A more detailed write up.
When I try to login using xbox live (to perform account linking) I am greeted with an error (the one that this thread is all about, expired ea credentials). No amount of account resetting for my EA account resolved this. This is because I was in or resetting the wrong EA account.
What happened for me was that years ago, back in the days of XBox 360 I played a game that needed Origin account, probably Assassins Creed Unity or something like that.If you read my unique EA ID here you will likely realise that this account is not something I wanted, it is entirely throwaway sign up to get into a stupid game in what feels like a million years ago... So I haven't been playing EA with Xbox in forever, I moved onto PC, Nintendo and Playstation somewhat, I had long forgotten about the account to the point that I made a new one with new e-mail and everything. Then gamepass shows up with EA Play offerings and here I am, I need to link my gamertag with EA (which I had done ages ago but completely forgot).
I am lucky that I still retain my old e-mail and can verify it. I can probably unlink this to my gamer tag and link my new account but meh.
For those who suspect that they may have a similar problem you can try to recover your old account as I have or maybe see if ea support can do an unlink for your xbox gamertag, assume the original ea account cannot be recovered and go from there.
Maybe check into your xbox 360 days and see if there are any EA games you played or your family played that may have forced an account you (this * should be against the law imo). Try to identify some info like what you played, etc. You might be able to use achievements for this. I don't know if MS has any info on what account is linked to the gamertag, it might be worth a check. Ea should at least be able to confirm the account has been inactive since forever. If you haven't moved maybe you can even try to confirm IP or something, see what can be done. Good luck.