Add customization for the Gemini Code Assist review bot

[kenzieschmoll]

Adds customization to the Gemini Code Assist bot to improve the quality of AI Reviews. This is a starting point inspired by the flutter/flutter and flutter/flutter-intellij configurations:

• https://github.com/flutter/flutter/tree/main/.gemini
• https://github.com/flutter/flutter-intellij/tree/main/.gemini

No tests required since this is an infra-only change.

Fixes #9773.

Pre-launch Checklist

General checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene wiki page, which explains my responsibilities.
• I read the Flutter Style Guide recently, and have followed its advice.
• I signed the CLA.
• I updated/added relevant documentation (doc comments with ///).

Issues checklist

• I listed at least one issue that this PR fixes in the description above.
• I listed at least one issue which has the contributions-welcome or good-first-issue label.
• I did not list at least one issue with the contributions-welcome or good-first-issue label. I understand this means my PR might take longer to be reviewed.

Tests checklist

• I added new tests to check the change I am making...
• OR there is a reason for not adding tests, which I explained in the PR description.

AI-tooling checklist

• I did not use any AI tooling in creating this PR.
• OR I did use AI tooling, and...
  • I read the AI contributions guidelines and agree to follow them.
  • I reviewed all AI-generated code before opening this PR.
  • I understand and am able to discuss the code in this PR.
  • I have verifed the accuracy of any AI-generated text included in the PR description.
  • I commit to verifying the accuracy of any AI-generated code or text that I upload in response to review comments.

Feature-change checklist

• This PR does not change the DevTools UI or behavior and...
  • I added the release-notes-not-required label or left a comment requesting the label be added.
• OR this PR does change the DevTools UI or behavior and...
  • I added an entry to packages/devtools_app/release_notes/NEXT_RELEASE_NOTES.md.
  • I included before/after screenshots and/or a GIF demo of the new UI to my PR description.
  • I ran the DevTools app locally to manually verify my changes.

If you need help, consider asking for help on Discord.

[gemini-code-assist]

Code Review

This pull request updates the project's documentation and configuration by removing Gemini logs from .gitignore and adding comprehensive guidelines to AGENTS.md regarding published packages, code quality, and documentation standards. Feedback suggests refining the method length rule to account for Flutter's declarative build methods and adjusting the documentation style for private members to maintain consistency with Effective Dart conventions.

[kenzieschmoll]

/gemini review

[gemini-code-assist]

Code Review

This pull request updates the project's documentation and contribution guidelines. Key changes include removing Gemini logs from .gitignore, adding new sections to AGENTS.md regarding published packages, code quality, documentation standards, and UI development best practices, and refining the phrasing and punctuation in STYLE.md. A minor formatting improvement was suggested for the pull request template reference in AGENTS.md to ensure consistency with the rest of the document.

[kenzieschmoll]

/gemini

[srawlins]

Love it!

[pq]

🎉