Switch from Node.js + pnpm to Bun runtime and package manager

Replace @libsql/client with bun:sqlite for zero-dependency SQLite access,
swap drizzle-orm/libsql adapter for drizzle-orm/bun-sqlite, and rewrite
Dockerfile to use oven/bun:1-alpine. The raw Database instance is no longer
exported via Proxy (native C++ methods lose `this` binding through
Reflect.get); instead, a closeDatabase() helper handles graceful shutdown
and the health check uses Drizzle's db.run() directly.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

package.json

@@ -3,9 +3,9 @@
   "version": "0.1.0",
   "private": true,
   "scripts": {
-    "dev": "next dev",
-    "build": "next build",
-    "start": "next start",
+    "dev": "bun --bun next dev",
+    "build": "bun --bun next build",
+    "start": "bun --bun next start",
     "lint": "biome check",
     "format": "biome format --write",
     "check-types": "tsc --noEmit",
@@ -16,10 +16,9 @@
   },
   "dependencies": {
     "@base-ui/react": "^1.2.0",
-    "@libsql/client": "^0.17.0",
-    "@tabler/icons-react": "^3.37.1",
+    "@tabler/icons-react": "^3.38.0",
     "@tanstack/react-hotkeys": "^0.3.1",
-    "better-auth": "^1.5.0",
+    "better-auth": "^1.5.2",
     "class-variance-authority": "^0.7.1",
     "clsx": "^2.1.1",
     "cmdk": "^1.1.1",
@@ -27,7 +26,7 @@
     "drizzle-orm": "1.0.0-beta.15-859cf75",
     "embla-carousel-react": "^8.6.0",
     "jotai": "^2.18.0",
-    "motion": "^12.34.3",
+    "motion": "^12.34.5",
     "next": "16.1.6",
     "node-vibrant": "^4.0.4",
     "react": "19.2.4",
@@ -44,7 +43,8 @@
     "zod": "^4.3.6"
   },
   "devDependencies": {
-    "@biomejs/biome": "2.4.4",
+    "@biomejs/biome": "2.4.5",
+    "@types/bun": "^1.3.10",
     "@tailwindcss/postcss": "^4.2.1",
     "@types/node": "^25.3.3",
     "@types/react": "^19.2.14",
@@ -53,5 +53,6 @@
     "drizzle-kit": "1.0.0-beta.15-859cf75",
     "tailwindcss": "^4.2.1",
     "typescript": "^5.9.3"
-  }
+  },
+  "packageManager": "bun@1.3.10"
 }