chore(deps): Bump @anthropic-ai/claude-code in /backend

Bumps [@anthropic-ai/claude-code](https://github.com/anthropics/claude-code) from 1.0.108 to 1.0.113.
- [Changelog](https://github.com/anthropics/claude-code/blob/main/CHANGELOG.md)
- [Commits](https://github.com/anthropics/claude-code/commits)

---
updated-dependencies:
- dependency-name: "@anthropic-ai/claude-code"
  dependency-version: 1.0.113
  dependency-type: direct:production
  update-type: version-update:semver-patch
...

Signed-off-by: dependabot[bot] <[email protected]>

Author: dependabot[bot]

backend/package-lock.json

@@ -54,7 +54,7 @@
     "prepublishOnly": "npm run build && npm run test"
   },
   "dependencies": {
-    "@anthropic-ai/claude-code": "1.0.108",
+    "@anthropic-ai/claude-code": "1.0.113",
     "@hono/node-server": "^1.0.0",
     "@logtape/logtape": "^1.0.0",
     "@logtape/pretty": "^1.0.0",
@@ -74,6 +74,6 @@
     "vitest": "^3.2.4"
   },
   "peerDependencies": {
-    "@anthropic-ai/claude-code": "1.0.108"
+    "@anthropic-ai/claude-code": "1.0.113"
   }
 }