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>

turbo.json

@@ -13,6 +13,7 @@
     },
     "lint": {},
     "format": {},
+    "format:check": {},
     "check-types": {},
     "test": {}
   }