There are two basic categories of Apps Script files -
Bound to the document (Sheet, Doc, Form)
Bound files do not show up in your Google Drive. Stand Alone Apps Scripts files do show up in your Google Drive.
You can create multiple projects inside of an Apps Script file, but projects in other files can not be searched or loaded into the code ...
According to Eric Koleda in Code.gs - date_add_and_subtract to make available the custom fuctions in an add-on it's required to include at least one add-on menu, but this is not working at this time.
There are a couple of related GAS issues, please star them:
"Test as add-on" from standalone project to Google Sheets doesn't link custom ...
Publish a Google Add-on to the G Suite Marketplace
You must use the G Suite Marketplace SDK in order to get to the
“Publish” section for publishing an add-on, and you must first open
the Google Cloud Platform for your specific project (apps script
The G Suite Marketplace SDK must be enabled in the Google Cloud
The two ...
A Google Apps Script web app will have it's own URL to be used to make HTTP GET/POST requests.
A G Suite Add-on adds a menu to a G Suite app (Google Docs, Google Forms, Google Sheets, Google Slides)
A Google Apps Script project could be bounded or standalone and could be used to post a G Suite add-on, a web app or both.
I tried to publish it with "Private visibility" but that didn't make it available to my other documents (tried searching in Add-ons > Get add-ons).
So how do I make the script available to use in all my documents?
Publishing and add-on as privately (unlisted or limited to a group of users) will not display the add-on on the add-ons store, except for ...
According to https://developers.google.com/gmail/add-ons/how-tos/publish to allow other users on your domain to install your add-on you should give them the deployment ID.
Publishing Gmail Add-ons
Publishing add-ons allows them to be used by other users. While a few
add-ons have been made available in the G Suite Marketplace for users