Add dependency duplication check between app and framework

Adds check-deps.ts which ensures backend/package.json doesn't duplicate
any dependencies already provided by backend/diachron/package.json.
Integrated into backend/check.sh.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/tsconfig.json

@@ -10,5 +10,5 @@
         "types": ["node"],
         "outDir": "out"
     },
-    "exclude": ["**/*.spec.ts", "**/*.test.ts"]
+    "exclude": ["**/*.spec.ts", "**/*.test.ts", "check-deps.ts"]
 }