How to fix Connection string is either blank or malformed - Azure Function App + Container

Question

I have a few functions in a Docker container that I'd like to deploy on Azure. One of them is triggered by additions to a Queue.

When building the container, I add the AZURE_STORAGE_CONNECTION_STRING as an ENV.

When I then run the container locally and add a job to the queue, the function inside the container picks it up and runs successfully. This tells me the connection string is in the container correctly, since that process has been triggered by a queue, and then also writes to some tables using the connection string.

However, I then push my container to ACR and use the CLI to create a function app and all the required resources. az functionapp create....

The functionapp deploys correctly, and even picks up jobs from the queue (so it must have some kind of connection string?), but when I go to write to a table, I get the error Connection string is either blank or malformed.

I have added the connection string to the app settings, redeployed, and tried 100 other things... It just won't work. Please help!