chore: update Docker build and dependencies

- Add .dockerignore for runtime state files (sqlite, logs, secrets)
- Bump Node.js base image from 18 to 20
- Add @types/better-sqlite3 dev dependency

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

package.json

@@ -77,6 +77,7 @@
     "zip-a-folder": "^3.1.9"
   },
   "devDependencies": {
+    "@types/better-sqlite3": "^7.6.13",
     "@types/chai": "^4.3.4",
     "@types/chai-string": "^1.4.5",
     "@types/cors": "^2.8.17",
@@ -93,4 +94,4 @@
     "typescript": "5.5.4"
   },
   "overrides": {}
-}
+}