Is it possible to expose a published Google Apps Script web-app from one tenant (domain) to another?
Solution 1:
You can try to create a Group in the Admin console of @example2.com with all the users in the Domain. After that, you can share the script with that Group.
Just make sure that the users OU (you can create a specific OU for it) have been allowed to share outside of the domain.
Or you can add it to a Share Drive and share it with the Group of domain @example2.com