Why can't I share/access my Photos library?

You can with Photos: Control (right) - click on a thumbnail and select "Edit with" in the contextual menu and select the editor of choice from the resulting list:

Other applications can access your Photos Library using the Media Browser.

But only one of your Photos Libraries will appear in the media browser - your System Photos Library.

To make your current Photos Library your system photos library, go to the Photos > Preferences > General and click "Use as System Photos Library", if I is not already greyed out.

After this, you should be seeing your photos and videos rom the System Photos Library, when you are using the photos browser in any external editor, that is fully compatible with Photos for Mac.

When you try to open an image file from an external edit, and when the File Chooser dialog appears, scroll down in the sidebar, until you are seeing "Media > Photos" in the sidebar. Click "Media > Photos" in the sidebar, then wait for the Photos Library to appear as an item. Click it, then wait for your Photos albums and folders to appear.

Very old external editors may not be able to perform the necessary protocol to access the Media Browser. If that happens. search for an update for the app in question.

We need more details - how are you trying to share with another app? What happens when you try - what error messages do you get?