Bungie doesn't have their own authentication servers. When you log in here you log in using the account credentials for the account you play Destiny on. So you'd log in using either PSN, Xbox, Battle.net, Steam, or Stadia credentials. The only email address kept at bungie.net would be the email you set up for receiving site notifications.

Several years ago, Bungie removed direct login through their own systems and switched to an authentication system that uses each platform's login authentication. While Bungie was making the switch, users had a chance to link an XBL ID or a PSN ID prior to the removal of the direct login methods. If you did not migrate to the new system of login at that time, then your previous Bungie.net profile no longer has a valid login and has been archived; it cannot be reclaimed. If you remember the profile, you can still view it, but you will be unable to log into it. - With the above being said, the switch from direct login methods happened quite a while ago. If you were still active in 2018 with your profile, you should be able to log into it with whichever XBL ID or PSN ID you had associated with it at the time. When Destiny 2 came out, Bungie was already using the platform authentication, so you may be misremembering the account(s) you have linked to your Bungie.net profile.