Problem with passkey for Apple ID, when logging to App Store Connect

Hello,

I started to have issues logging on my Safari browser to my developer's account on App Store Connect. So far I haven't had any problems. I just clicked on the "email or phone number" field, my appleID was suggested, I used finger tips reader and that was it. No more interactions from my side. I was logged in.

Recently I have bought and setup new iPhone with FaceID. I do not know if it has anything to do, but it appears I have problems since that moment. Previously I used old iPhone SE (2020), without Face ID, but with fingertips reader.

Now, when I try to log in the same window appear, but after clicking in the "email or phone number" a passkey for my appleID is suggested (I am not sure what was previously suggested: passkey or password?). The issue starts when I use my fingertips reader - I get "Can't verify your account. Try again or continue with password" message. It looks like in the attached screenshot.

When I choose "Other accounts..." option and pick the same appleID but with password, everything works. I need, however, to click twice (first the user, then the password) and sometimes additionally 2FA code is displayed (on the same macOS), which I have to copy to the Safari browser to confirm my account! This is working, but very annoying.

Is there a way to resolve this issue? I do not know - fix the passkey, get rid of using passkey as default option when logging to App Store Connect? Any other way?