Apple doesn’t concern a password on your personal emails. You solely have a password on your AppleID and that by no means is shared with different firms.
Personal relay isn’t technically the identical as Check in with Apple or Conceal My Electronic mail aside from all of them are bundled with iCloud+
If you happen to create an account with one other service, it’s as much as that service to combine with passcode by way of Check in with Apple the place your machine will use your most important iCloud credentials to unlock a Cross Key token saved in your machine and ship that token (which isn’t your AppleID or iCloud password) to log you in.
If that service (chatGPT in your case) forces you to decide on a password, it’s probably you used Conceal My Electronic mail solely and no matter you selected to ship to them for them to retailer and authenticate. Once more, this isn’t your AppleID password except you reused it.
If you happen to aren’t certain which path the service allow you to select, examine with chatGPT buyer assist. Or you could possibly strive their password reset process which generally emails a reset hyperlink or makes use of SMS / two issue auth.
You completely gained’t use iforgot.apple.com in any case the place you’ve a non-public alias or passcode despatched to a 3rd get together. Solely use “iforgot” should you can’t log in to https://appleid.apple.com along with your Apple credentials.