Fix nightly build of the staging cirq website

[pavoljuhas]

• Fix syntax error in docs/noise/_index.yaml
• Stop including deleted yaml file
• Format with the yaml_format Google tool

Fixes #6587

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 97.81%. Comparing base (3b975b0) to head (602e3cb). Report is 1 commits behind head on main.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #6615 +/- ## ========================================== - Coverage 97.81% 97.81% -0.01% ========================================== Files 1063 1063 Lines 91761 91761 ========================================== - Hits 89759 89755 -4 - Misses 2002 2006 +4 ```

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