EA / XBOX account don't match

@Rotblut  I have correctly linked my EA account and my XBOX account.
But it still doesn't work.

Why is it necessary to link your XBOX and EA account? I bought Battlefield 3 many years ago (with Origin) and it worked fine.
Since the adding of BF3 on the "Game Pass", it does not work anymore ...

By the way, I don't know if this has any impact, but my EA and XBOX email addresses are not the same.
I don't think it's a problem, but I'll mention it anyway.

And why do I get this error message for Battlefield 3, but not for Battlefield 5 ?

What if I don't want the XBOX account anymore? Can't I just unlink it?

I bought Battlefield 1, 3, 4 and 5 on Steam and all the others work without any issues (also Mass Effect Legendary edition works), but when launching Battlefield 3 it gives a message "Xbox and EA accounts don't match" and refuses to start while waiting for Origin client which is actually running already. I don't recall I have ever played it on Xbox (I have played 1 and 4 though), so what's the rationale of the message and even if I had what's the issue, since connected account is the correct one. I actually just linked it on Origin client thinking it would solve the issue, but no luck. I checked out linking on Xbox/Microsoft side also and it's valid. I also noticed on Battlefeed view on the browser that I have played Battlefield 4 ten months ago on Xbox, which is correct and also based on that linking should be ok.

Is it really so, that even if I would buy Battlefield 3 on Origin instead of Steam, it wouldn't work on PC due to some Xbox related issue, and why the functionality of the PC version is dependent on the Xbox in the first place?

Actually now it began to work for some reason ¯\_(ツ)_/¯