By default, Apps Script creates a hidden GCP project that operates in the background. Therefore, if you want Apps Script to interact with other GCP services (Cloud Run Function), you need to move the Apps Script execution to your target GCP project.

Guillaume blaquiere's Medium article provides a guide on how to call Google Cloud Run from Apps Script. While I have not tested it myself, I’ve observed that many people have resolved similar concerns using the article. Although the article focuses on Cloud Run, it shares the same infrastructure as Cloud Functions. It might work for you as well.