What can I do?
This is a simple issue that can be quickly rectified by following the steps below:
Go ahead and create a new account using whatever authentication service you were using previously. Make a note of the profile URL - you can get to the new profile by clicking on your user name at the top of the page. Keep this handy.
Locate your original ...
The message is real. Its content matches the post Support for OpenID ends on July 25, 2018 by a Stack Exchange employee.
It was not sent to all participants, only to those whose login method is being phased out. Another SE employee tweeted:
Heads up: we're about to send an email out to about 120,000 users who only have an OpenID to login to Stack ...
It seems there are two users called passerby51, one who has been a memeber for 53 days, the other has been a memeber for 2.5 years, and has 6 questions and an answer. If both of these are you, request that the two accounts be merged.
see How do I combine my two accounts?
I haven't managed to reproduce the effect you're describing.
I'm not computer-savvy either, but this is what I see when I go to MathOverflow in a window where the history doesn't show I'm already logged in (e.g., a private window). In the menu up at the top there's a Log In button, next to Sign Up. Here I'm using FireFox 60.0.2.
(If I'm already logged in ...
Right now (December 2018), the answer is: there is a striped "speech balloon" icon on the top right of the page, and clicking it will reveal a menu with a "log out" link.
I imagine the answer to this question may continue to change over time, as Stack Exchange continues to redesign the user interface. The current answer can be found at this page: How to ...
You can just use the "click here to recover your account" link on the login page. You should then receive an email with a link to a form to set a new password. Afterwards you should be able to log in by choosing "log in with Stack Exchange".