Hello ,
This is applicable for function apps running on dedicated app service plan however for apps running on consumption and premium plan, there are additional settings that needs to be added WEBSITE_CONTENTAZUREFILECONNECTIONSTRING with storage account connection string value and WEBSITE_CONTENTSHARE with storage account fileshare name. Please note that these settings are not applicable for Linux plans.
So The limitation is on the Azure Files side which is used by Consumption and EP plans for dynamic scaling.
The following issue has more info on this matter: Managed identity support for WEBSITE_CONTENTAZUREFILECONNECTIONSTRING setting
Please "Accept Answer" if the answer is helpful so that others in the community may benefit from your experience.
Thanks
Deepanshu