@Alistair Young Thanks for reaching out.
I will suggest you to review the Diagnose and solve problems blade on your function app to know more details on the 500 error. Looks like there might be some dependency missing or your have configure some application setting in your local.setting.json which is not configured in your function app application setting blade which would cause this behavior. There could be multiple other reasons for the 500 error but reviewing the application insights logs/ diagnose and solve problem blade will give you more insights on the issue and the steps to resolve the issue if there are any.
In case if you need any assistance then please let me know.