Typecheck and lint example client

Don't do server yet, since it has its own package.json which breaks
checking imports.

tsconfig.json

@@ -9,6 +9,6 @@
     "skipLibCheck": true,
     "forceConsistentCasingInFileNames": true
   },
-  "include": ["src/**/*"],
+  "include": ["src/**/*", "examples/clients/typescript/**/*"],
   "exclude": ["node_modules"]
 }