chore(deps): bump @anthropic-ai/claude-agent-sdk from 0.2.47 to 0.2.62

Bumps [@anthropic-ai/claude-agent-sdk](https://github.com/anthropics/claude-agent-sdk-typescript) from 0.2.47 to 0.2.62.
- [Release notes](https://github.com/anthropics/claude-agent-sdk-typescript/releases)
- [Changelog](https://github.com/anthropics/claude-agent-sdk-typescript/blob/main/CHANGELOG.md)
- [Commits](anthropics/claude-agent-sdk-typescript@v0.2.47...v0.2.62)

---
updated-dependencies:
- dependency-name: "@anthropic-ai/claude-agent-sdk"
  dependency-version: 0.2.62
  dependency-type: direct:production
  update-type: version-update:semver-patch
...

Signed-off-by: dependabot[bot] <support@github.com>

Author: dependabot[bot]

package.json

@@ -21,7 +21,7 @@
   "packageManager": "pnpm@10.26.0",
   "dependencies": {
     "@agentclientprotocol/sdk": "^0.14.1",
-    "@anthropic-ai/claude-agent-sdk": "^0.2.42",
+    "@anthropic-ai/claude-agent-sdk": "^0.2.62",
     "@modelcontextprotocol/sdk": "^1.26.0",
     "@tailwindcss/typography": "^0.5.19",
     "@xterm/addon-fit": "^0.11.0",