Currently in Google Cloudrun when a access to service is restricted it provides below error message. Is it possible to customize the error message as like CloudFlare (https://support.cloudflare.com/hc/en-us/articles/200172706-Configuring-Custom-Pages-Error-and-Challenge-)?
This error message doesn't not come from Cloud Run service, but the bloc before, that check the authentication (named GFE - Google Front End).
You can't customise that part.