chore: bootstrap repository tooling

Add npm and Bun dependency metadata.

Configure TypeScript and shared editor defaults.

Ignore dependencies, build output, caches, logs, and local files.

package.json

@@ -0,0 +1,29 @@
+{
+  "private": true,
+  "type": "module",
+  "bin": {
+    "base-ui-tailwind": "./cli/index.mjs"
+  },
+  "scripts": {
+    "cli": "node ./cli/index.mjs",
+    "generate:manifest": "node scripts/generate-manifest.mjs",
+    "typecheck": "tsc --noEmit",
+    "check:exports": "node scripts/check-ui-exports.mjs",
+    "check": "npm run typecheck && npm run check:exports"
+  },
+  "dependencies": {
+    "@base-ui/react": "^1.6.0",
+    "cac": "^7.0.0",
+    "clsx": "^2.1.1",
+    "lucide-react": "^1.23.0",
+    "tailwind-merge": "^3.6.0",
+    "tailwindcss": "^4.3.2",
+    "tw-animate-css": "^1.4.0",
+    "vite": "^8.1.3"
+  },
+  "devDependencies": {
+    "@types/react": "^19.2.17",
+    "@types/react-dom": "^19.2.3",
+    "typescript": "^6.0.3"
+  }
+}