I was also struggling with that same error message [firebase_functions/unauthenticated] >UNAUTHENTICATED. In my case, there was a policy at the organization level that required all calls to Cloud Run functions to be authenticated by IAM and for users to belong to the organization, so I could not add the allUsers principal to the function. Instead, I had to turn off the IAM authentication for the function, which can be done by selecting the function and in the security tab, uncheck "Use IAM to authenticate incoming requests.

Note that during deployment of the function, you may still get an error message that the IAM could not be changed to public, this is fine, the function is deployed, you just need to apply that change afterwards.

Official Google documentation and thanks to Tom Elliott for pointing me towards the solution.

Uncheck IAM Authentication in the Security tab of the function