refactor: replace Biome with oxlint + oxfmt

Migrate the entire monorepo from Biome 2.4.7 to oxlint 1.56.0 (linter)
and oxfmt 0.41.0 (formatter) for faster lint/format and broader rule
coverage.

- Add `.oxlintrc.json` with React, TypeScript, unicorn, import plugins
  and correctness/suspicious categories
- Add `.oxfmtrc.json` with 2-space indent, import sorting, and Tailwind
  class sorting (all 30+ custom className attributes migrated)
- Add `docs/.oxlintrc.json` and `docs/.oxfmtrc.json` with Next.js plugin
- Update all 12 workspace package.json scripts: `oxlint`, `oxfmt`,
  `oxfmt --check`
- Add `format:check` turbo task and CI step
- Update VS Code settings/extensions to use `oxc.oxc-vscode`
- Update CI path triggers from `biome.json` to new config files
- Remove all `biome-ignore` comments and fix shadowed variables
- Delete `biome.json` and `docs/biome.json`
- Reformat entire codebase with oxfmt

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

.github/workflows/claude-code-review.yml

@@ -36,9 +36,8 @@ jobs:
         uses: anthropics/claude-code-action@v1
         with:
           claude_code_oauth_token: ${{ secrets.CLAUDE_CODE_OAUTH_TOKEN }}
-          plugin_marketplaces: 'https://github.com/anthropics/claude-code.git'
-          plugins: 'code-review@claude-code-plugins'
-          prompt: '/code-review:code-review ${{ github.repository }}/pull/${{ github.event.pull_request.number }}'
+          plugin_marketplaces: "https://github.com/anthropics/claude-code.git"
+          plugins: "code-review@claude-code-plugins"
+          prompt: "/code-review:code-review ${{ github.repository }}/pull/${{ github.event.pull_request.number }}"
           # See https://github.com/anthropics/claude-code-action/blob/main/docs/usage.md
           # or https://code.claude.com/docs/en/cli-reference for available options
-

.github/workflows/claude.yml

@@ -47,4 +47,3 @@ jobs:
           # See https://github.com/anthropics/claude-code-action/blob/main/docs/usage.md
           # or https://code.claude.com/docs/en/cli-reference for available options
           # claude_args: '--allowed-tools Bash(gh pr:*)'
-

.github/workflows/docker.yml

@@ -11,7 +11,8 @@ on:
       - "turbo.json"
       - "package.json"
       - "bun.lock"
-      - "biome.json"
+      - ".oxlintrc.json"
+      - ".oxfmtrc.json"
       - "tsconfig.json"
       - ".github/workflows/docker.yml"
     tags: ["v*"]

.github/workflows/test.yml

@@ -12,6 +12,11 @@ jobs:
       - name: Checkout
         uses: actions/checkout@v4
 
+      - name: Setup Node
+        uses: actions/setup-node@v4
+        with:
+          node-version: 24
+
       - name: Setup Bun
         uses: oven-sh/setup-bun@v2
 
@@ -25,6 +30,9 @@ jobs:
       - name: Lint
         run: bunx turbo run lint
 
+      - name: Format check
+        run: bunx turbo run format:check
+
       - name: Type check
         run: bunx turbo run check-types