I struggled how to make an authenticated call from Apps Scripts to Cloud Run even though I had owner rights on the GCP project. This post describes how to do it without reinventing the wheel.
Some very useful setup tips for using Cloud Run with Google Apps Scripts including additional references if you are keen to explore more.
Source: How to call Google Cloud Run (or Cloud Functions) from Apps Scripts
Member of Google Developers Experts Program for Google Workspace (Google Apps Script) and interested in supporting Google Workspace Devs.