Support using a different gcp project for gemini api calls that isn't the workload ID project

TL;DR

The way the workflow is written makes it impossible to auth via workload id to one project and configure gemini to use a different project for API calls.

My service account is in a different project than the one where the gemini api is enabled

You made this impossible because you directly reference the output of the shared workflows workload id step here: https://github.com/google-github-actions/run-gemini-cli/blob/c27fb3eed34c68e75f9dd6400384f56b1f1633d4/action.yml#L225

If you had just made that an optional input I could configure workload id myself and pass in the token, but because its hard coded like this I would have to fork the entire thing.

Expected behavior

It should be possible to set the auth project independently from the gemini project

Observed behavior

No response

Action YAML

Use with workload id as intended

Log output

Additional information

No response

Inspect action.yml around line 225 and the workload identity configuration it references. Trace how authentication and Gemini project settings are passed; done means callers can select the authentication and Gemini API projects independently while preserving the existing workload identity flow.