refactor(node): migrate from better-sqlite3 to node:sqlite, require Node 24+

Native binding caused install pain on every new Node major (no prebuilts +
node-gyp needs VS+Windows SDK to fall back). For this project's workload
(a few ops/day, no advanced SQLite features) better-sqlite3's perf edge is
irrelevant — node:sqlite's bundled, ABI-stable sync API is the better fit.

- db.ts: DatabaseSync, db.exec("PRAGMA …"), explicit BEGIN/COMMIT helper to
  replace db.transaction(); row casts go through unknown because node:sqlite
  returns Record<string, SQLOutputValue>.
- package.json: drop better-sqlite3 + @types/better-sqlite3, bump
  engines.node to >=24, vitest 2 → 4 (2.x couldn't resolve `node:sqlite`).
- mailbox-doctor: add Step 1 that enforces Node ≥24 with a concrete fix
  message, renumbers downstream steps.

Node 1.2.0 → 1.3.0. 35 transitive packages removed from the lockfile.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

node/package.json

@@ -1,6 +1,6 @@
 {
   "name": "@kuns/claude-mailbox",
-  "version": "1.2.0",
+  "version": "1.3.0",
   "description": "Standalone MCP mail server that lets parallel Claude sessions coordinate with each other.",
   "type": "module",
   "bin": {
@@ -20,11 +20,10 @@
     "prepack": "npm run build"
   },
   "engines": {
-    "node": ">=20"
+    "node": ">=24"
   },
   "dependencies": {
     "@modelcontextprotocol/sdk": "^1.29.0",
-    "better-sqlite3": "^11.3.0",
     "commander": "^12.1.0",
     "fastify": "^5.0.0",
     "zod": "^3.25.0"
@@ -33,10 +32,9 @@
     "node-windows": "^1.0.0-beta.8"
   },
   "devDependencies": {
-    "@types/better-sqlite3": "^7.6.11",
     "@types/node": "^22.7.4",
     "typescript": "^5.6.2",
-    "vitest": "^2.1.1"
+    "vitest": "^4.1.6"
   },
   "keywords": [
     "mcp",