To run the example function app locally from VSCode, make sure to install the Azure Functions and Azurite extensions.
Then start Azurite via the Azurite: Start VSCode task.
Build the library npm run build or use npm run watch to hotdeploy changes. (Warning: This didn't always work for me in practice.)
Start the function app by running the VScode launch configuration Debug Functions app.
Then send some requests to the API, for example:
curl -X POST -H "Content-Type: application/json" -d '{"name":"hi"}' http://localhost:7071/api/users