Can't log into the old school website without having a Jagex account?

Hi, here's my issue.

I have a jagex account "[[email protected]](mailto:[email protected])" and also I have a runescape account with login "[[email protected]](mailto:[email protected])", which is not connected to the jagex account (but I have other accounts connected to that jagex acc).

Also, the "[[email protected]](mailto:[email protected])" email is registered to the runescape account "[[email protected]](mailto:[email protected])".

I'm unable to log in via the game because I need authenticator (which I don't have anymore).

I find it impossible to log into account settings panel through the links you posted. It pushes me to jagex account login every time and logging "via runescape username" and using my email there won't work

Is it simply not possible and my account is gone?