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>

packages/config/.oxlintrc.json

@@ -0,0 +1,4 @@
+{
+  "$schema": "../../node_modules/oxlint/configuration_schema.json",
+  "extends": ["../../.oxlintrc.json"]
+}

packages/config/package.json

@@ -6,6 +6,12 @@
   "exports": {
     ".": "./src/index.ts"
   },
+  "scripts": {
+    "lint": "oxlint",
+    "format": "oxfmt --config ../../.oxfmtrc.json",
+    "format:check": "oxfmt --check --config ../../.oxfmtrc.json",
+    "check-types": "tsc --noEmit"
+  },
   "devDependencies": {
     "@types/bun": "catalog:",
     "typescript": "catalog:"

packages/config/src/index.ts

@@ -4,8 +4,7 @@ import path from "node:path";
 
 export const DATA_DIR = path.resolve(process.env.DATA_DIR || "./data");
 
-export const DATABASE_URL =
-  process.env.DATABASE_URL || path.join(DATA_DIR, "sqlite.db");
+export const DATABASE_URL = process.env.DATABASE_URL || path.join(DATA_DIR, "sqlite.db");
 
 export const CACHE_DIR = process.env.CACHE_DIR
   ? path.join(process.env.CACHE_DIR, "images")
@@ -17,8 +16,6 @@ export const AVATAR_DIR = path.join(DATA_DIR, "avatars");
 
 // ─── TMDB ────────────────────────────────────────────────────
 
-export const TMDB_API_BASE_URL =
-  process.env.TMDB_API_BASE_URL || "https://api.themoviedb.org/3";
+export const TMDB_API_BASE_URL = process.env.TMDB_API_BASE_URL || "https://api.themoviedb.org/3";
 
-export const TMDB_IMAGE_BASE_URL =
-  process.env.TMDB_IMAGE_BASE_URL || "https://image.tmdb.org/t/p";
+export const TMDB_IMAGE_BASE_URL = process.env.TMDB_IMAGE_BASE_URL || "https://image.tmdb.org/t/p";