OpenID (like Yahoo) isn't supported any more. You need to add a Google, Facebook, or email-based sign-in to your account while you're still logged in. You were able to ask this question, so presumably you're logged in on Meta. Add a credential, and then use that to log in to your linked account elsewhere.
I've been getting randomly logged out of sites for the last day or so, after months of no disruption, so if you're relying only on an OpenID account, get an alternative in place quickly in case you get logged out here. The help still refers to OpenID including Yahoo, but aside from that incorrect text, the instructions for how to add credentials are still good.
Regarding your update: the other login you show (last used in 2014) has what looks like a generic OpenID icon. Even though the ID appears to be an email address, that's not an SE email-based login. For comparison, here's what mine look like. The first one is an email login that I created specifically for SE when they announced that OpenID would be going away. Note the SE icon, in contrast to the icon on yours. As you can tell, I don't use it much -- it's my backup in case Google should ever fail me. SE did not previously allow adding an email login to an account that had some other credential; they changed that when they deprecated OpenID, to allow those of us who only had one of Google or Facebook to still have a backup method of logging in.