ci: add CI workflow for format, typecheck, and test

Runs on push/PR to main. Also adds skipLibCheck to tsconfig to silence
pre-existing errors in vite/vitest declaration files that don't affect
the Worker build.

Co-Authored-By: Claude Sonnet 4.6 <[email protected]>

tsconfig.json

@@ -11,7 +11,8 @@
     "noEmit": true,
     "isolatedModules": true,
     "allowJs": true,
-    "forceConsistentCasingInFileNames": true
+    "forceConsistentCasingInFileNames": true,
+    "skipLibCheck": true
   },
   "include": ["src/**/*"],
   "exclude": ["node_modules", "dist"]