dx: Add Claude Code GitHub Workflow (#10099)

## 🤖 Installing Claude Code GitHub App

This PR adds a GitHub Actions workflow that enables Claude Code
integration in our repository.

### What is Claude Code?

[Claude Code](https://claude.ai/code) is an AI coding agent that can
help with:
- Bug fixes and improvements  
- Documentation updates
- Implementing new features
- Code reviews and suggestions
- Writing tests
- And more!

### How it works

Once this PR is merged, we'll be able to interact with Claude by
mentioning @claude in a pull request or issue comment.
Once the workflow is triggered, Claude will analyze the comment and
surrounding context, and execute on the request in a GitHub action.

### Important Notes

- **This workflow won't take effect until this PR is merged**
- **@claude mentions won't work until after the merge is complete**
- The workflow runs automatically whenever Claude is mentioned in PR or
issue comments
- Claude gets access to the entire PR or issue context including files,
diffs, and previous comments

### Security

- Our Anthropic API key is securely stored as a GitHub Actions secret
- Only users with write access to the repository can trigger the
workflow
- All Claude runs are stored in the GitHub Actions run history
- Claude's default tools are limited to reading/writing files and
interacting with our repo by creating comments, branches, and commits.
- We can add more allowed tools by adding them to the workflow file
like:

```
allowed_tools: Bash(npm install),Bash(npm run build),Bash(npm run lint),Bash(npm run test)
```

There's more information in the [Claude Code
documentation](http://docs.anthropic.com/s/claude-code-github-actions).

After merging this PR, let's try mentioning @claude in a comment on any
PR to get started!

.github/workflows/claude.yml

@@ -0,0 +1,47 @@
+name: Claude Code
+
+on:
+  issue_comment:
+    types: [created]
+  pull_request_review_comment:
+    types: [created]
+  issues:
+    types: [opened, assigned]
+  pull_request_review:
+    types: [submitted]
+
+jobs:
+  claude:
+    if: |
+      (
+        (github.event_name == 'issue_comment' && contains(github.event.comment.body, '@claude')) ||
+        (github.event_name == 'pull_request_review_comment' && contains(github.event.comment.body, '@claude')) ||
+        (github.event_name == 'pull_request_review' && contains(github.event.review.body, '@claude')) ||
+        (github.event_name == 'issues' && (contains(github.event.issue.body, '@claude') || contains(github.event.issue.title, '@claude')))
+      ) && (
+        github.event.comment.author_association == 'OWNER' ||
+        github.event.comment.author_association == 'MEMBER' ||
+        github.event.comment.author_association == 'COLLABORATOR' ||
+        github.event.review.author_association == 'OWNER' ||
+        github.event.review.author_association == 'MEMBER' ||
+        github.event.review.author_association == 'COLLABORATOR' ||
+        github.event.issue.author_association == 'OWNER' ||
+        github.event.issue.author_association == 'MEMBER' ||
+        github.event.issue.author_association == 'COLLABORATOR'
+      )
+    runs-on: ubuntu-latest
+    permissions:
+      contents: read
+      pull-requests: read
+      issues: read
+      id-token: write
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 1
+      - name: Run Claude Code
+        id: claude
+        uses: anthropics/claude-code-action@beta
+        with:
+          anthropic_api_key: ${{ secrets.ANTHROPIC_API_KEY }}