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>

biome.json

@@ -1,5 +1,5 @@
 {
-  "$schema": "https://biomejs.dev/schemas/2.4.4/schema.json",
+  "$schema": "./node_modules/@biomejs/biome/configuration_schema.json",
   "vcs": {
     "enabled": true,
     "clientKind": "git",