Flake in auth test calling `language.v2.LanguageService/AnalyzeSentiment`

[github-actions]

Failure in Google Cloud Build on main:

• Build: gcb-pm-auth-integration (rust-auth-testing)
• Build Log: https://console.cloud.google.com/cloud-build/builds;region=us-central1/caedab10-7b52-424a-9cc4-cd00e30aeed8?project=977362148892
• Commit: 7870c84

Associated Pull Requests:

• chore: update sources and regenerate #6138

[github-actions]

@googleapis/cloud-sdk-rust-team A critical issue has been created, please respond immediately.

[dbolduc]

failures:
---- driver::run_api_key stdout ----
full error: the request exceeded the request deadline error sending request for url (https://language.googleapis.com/v2/documents:analyzeSentiment?%24alt=json%3Benum-encoding%3Dint)
Caused by:
    0: error sending request for url (https://language.googleapis.com/v2/documents:analyzeSentiment?%24alt=json%3Benum-encoding%3Dint)
    1: operation timed out
  because: Error { kind: Timeout, source: Some(reqwest::Error { kind: Request, url: "https://language.googleapis.com/v2/documents:analyzeSentiment?%24alt=json%3Benum-encoding%3Dint", source: TimedOut }) }
  because: reqwest::Error { kind: Request, url: "https://language.googleapis.com/v2/documents:analyzeSentiment?%24alt=json%3Benum-encoding%3Dint", source: TimedOut }
  because: TimedOut
Error: the request exceeded the request deadline error sending request for url (https://language.googleapis.com/v2/documents:analyzeSentiment?%24alt=json%3Benum-encoding%3Dint)
Caused by:
    0: error sending request for url (https://language.googleapis.com/v2/documents:analyzeSentiment?%24alt=json%3Benum-encoding%3Dint)
    1: operation timed out
failures:
    driver::run_api_key