How to track people who are logged in to the site?

Question

Google Analytics

Hello colleagues.
I am new to analytics and do not understand much yet, but there are tasks for which I must turn to you for solutions!

I want to use GTM to track users who have logged in to the site. In order to understand how many visitors and how many potential customers. But I ran into the following problems:
1. There are several options for authorization Google, Facebook, Log in. (They are united by the /ru/login/ page)
At first, I thought to bind to an element on the page that all authorized users have by default (Profile picture.)
That is, as soon as a person logs in, he appears (Profile picture.) And I catch him with analytics by the presence of this picture. But the problem is that there are people who are already logged in and when they roam the site of the analyst, on each of the pages they catch (Profile picture.), respectively, I will get incorrect distorted analytics.