Access to a shared library has two parts: who is a member and what they can do, and whether people outside that membership can see the library at all.
Both are managed by a Manager of the library.
The three roles
Viewer can open the library and use what is in it, but cannot change it.
Editor can add, edit and organise content.
Manager can do everything an Editor can, plus rename the library, change its access, manage members, and delete it.
Add people by searching for them, then set each person's role. You can change or remove someone's role later from the same place.
General access
Alongside membership, each library has a general access setting:
Private. Only members can find and open the library.
Org visible. Every educator in your organisation can find and view the library.
Org visible is a good fit for a library of resources you want everyone to be able to draw on. It gives colleagues who are not members the same abilities as a Viewer, so they can use the content without being able to change it. To let someone contribute, add them as an Editor.
Who does not get access automatically
Being an organisation administrator does not by itself grant access to a shared library. Administrators need to be added as members like anyone else, or the library needs to be set to Org visible. This is deliberate, so that a private library stays private.