chore: update biome config and format commands

- Exclude tailwind.css from linter includes
- Add biome lint to format commands

biome.jsonc

@@ -64,6 +64,8 @@
   },
   "linter": {
     "enabled": true,
+    "includes": ["!**/tailwind.css"],
+    // only enable sorted tailwind css rule. used as formatter instead of linter
     "rules": {
       "nursery": {
         // to sort tailwind css classes

package.json

@@ -65,8 +65,8 @@
     "test:e2e": "yarn playwright test",
     "test:lint": "eslint . --ext .js,.jsx,.cjs,.mjs,.ts,.tsx,.cts,.mts",
     "test:scripts": "vitest scripts",
-    "format": "biome format --write",
-    "format:check": "biome format",
+    "format": "biome format --write && biome lint --write",
+    "format:check": "biome format && biome lint",
     "lint": "eslint . --ext .js,.jsx,.cjs,.mjs,.ts,.tsx,.cts,.mts --fix && yarn typecheck && yarn check:i18n",
     "prepare": "git config blame.ignoreRevsFile .git-blame-ignore-revs && husky",
     "claude": "dotenv -e .env -- claude"