When I and my teammates set up to collaborate, we all git clone a shared repo--something like this...

$ git clone https://github.com/org-or-user/the-team-repo   # Make local copy of repo
$ git checkout main   # Point HEAD at "main", i.e., make "main" my current branch

In this way, we all start with the same understanding of where branch main is--the commit represented by the green circle.

Key Learning Points:

The origin/main branch, seen in both local repos, is a "tracking branch". git uses it to keep track of where the main branch on the remote called "origin" is pointing.

As you will see, this tracking is not "live"; no automatic cross-repo notification is happening.

I normally have no reason to git checkout a tracking branch like origin/main. Its value in my repo is updated when I git push and git pull.