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/README.md

@@ -48,5 +48,5 @@ Cost: one local HTTP round-trip plus Node coldstart per prompt (~100ms on Window
     npm config set //git.kuns.dev/api/packages/releases/npm/:_authToken=<token>
     ```
 
-`gyp ERR! find VS` on Windows during install
-:   `better-sqlite3` ships prebuilt binaries for current Node LTS versions. If yours isn't covered, npm falls back to building from source and needs the Visual Studio Build Tools. Either install them or pin to a Node version with a matching prebuild.
+`Cannot find module 'node:sqlite'` or similar
+:   claude-mailbox uses Node's built-in `node:sqlite`, stable since Node 24. On Node 22.5–23.x it works only with `--experimental-sqlite`. Upgrade to Node 24 LTS or newer: `nvm install 24 && nvm use 24` (or `winget install OpenJS.NodeJS.LTS` on Windows).