@Morten Bloch Lundgreen , To assist you better on this, could you please more info about your WebApp and Function App? How exactly are the functions called? Which OS/hosting plan are you leveraging? What exactly happens? Do you receive any error message?
Some configuration settings are slot-specific (is sticky setting - meaning, the setting is targeted to a slot and is not swapped). Kindly see if this is the case-
Slots docs -which settings are swapped | Azure Functions and Azure WebApps
Also, to begin with (if you haven’t done this already so), you may Diagnose and solve problems feature from Azure Portal.
To do this, navigate to your function app/Web App in the Azure portal.
Select Diagnose and solve problems to open Azure Functions diagnostics.
Note: Kindly do not share any PII data on the public forum.