Add App <-> AppBridge tests, setHostContext & sendToolInputPartial (#55)

* Add App <-> AppBridge integration tests

- Add minimalistic tests validating communication between App (guest) and AppBridge (host)
- Test initialization handshake flow
- Test Host -> App notifications (toolInput, toolInputPartial, toolResult, hostContext)
- Test App -> Host notifications (sizeChange, log)
- Test App -> Host requests (sendMessage, sendOpenLink)
- Test ping functionality
- Add setHostContext and sendToolInputPartial to AppBridge
- Add test script to package.json

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

* docs: add JSDoc for setHostContext and sendToolInputPartial

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

* fix: add @types/bun for test type checking

- Add @types/bun devDependency for bun:test types
- Fix mock client request return type

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

---------

Co-authored-by: Claude <noreply@anthropic.com>

package.json

@@ -30,6 +30,7 @@
     "start:example-mcp-server": "cd examples/simple-server && npm start",
     "start": "NODE_ENV=development npm run build && concurrently 'npm run start:example-host' 'npm run start:example-mcp-server'",
     "build": "bun build.bun.ts",
+    "test": "bun test",
     "prepare": "npm run build && husky",
     "docs": "typedoc",
     "docs:watch": "typedoc --watch",
@@ -39,6 +40,7 @@
   },
   "author": "Olivier Chafik",
   "devDependencies": {
+    "@types/bun": "^1.3.2",
     "@types/react": "^19.2.2",
     "@types/react-dom": "^19.2.2",
     "concurrently": "^9.2.1",