Hello JDR
Your Azure function even if it contains others triggers besides HTTP, will run locally, since you may have installed storage simulations like Azurite. However, to run Azure functions in the cloud, it needs additional information and resources like a storage account (where its own binaries) may lie.
The proper way to deploy Azure functions on cloud is not from Visual Studio but using a proper Infrastructure-as-code (IaC) templates, like Azure Bicep (Or Terraform, if you are doing multi-cloud).
The following step-by-step tutorial may help you. Try this, and then add your code accordingly.
https://learn.microsoft.com/en-us/azure/azure-functions/functions-best-practices?tabs=csharp