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/logger/.oxlintrc.json

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

packages/logger/package.json

@@ -7,8 +7,9 @@
     ".": "./src/index.ts"
   },
   "scripts": {
-    "lint": "biome check",
-    "format": "biome format --write",
+    "lint": "oxlint",
+    "format": "oxfmt --config ../../.oxfmtrc.json",
+    "format:check": "oxfmt --check --config ../../.oxfmtrc.json",
     "check-types": "tsc --noEmit"
   },
   "dependencies": {

packages/logger/src/index.ts

@@ -31,10 +31,7 @@ export interface Logger {
   debug(msg: string, ...args: unknown[]): void;
 }
 
-function wrapLevel(
-  child: pino.Logger,
-  lvl: "error" | "warn" | "info" | "debug",
-) {
+function wrapLevel(child: pino.Logger, lvl: "error" | "warn" | "info" | "debug") {
   return (msg: string, ...args: unknown[]) => {
     if (args.length === 0) {
       child[lvl](msg);