This is how I resolved the issue in my side: I found out that we had a policy on our subscription that prevented us from creating a storage account which allows local authentication (key based), and this is why every time I tried to change the configuration, it went back off.
The issue is that by default, when you create a function app, it is being created with a storage account, that the authentication between it and the function app is key based. So, the resolution was to create a function app that will communicate with the storage account based on MSI (and not key based), and this unblocked me from deploying the function app using Azure CLI, or Visual Studio.
In order to do it, I followed this documentation: Use managed identity instead of AzureWebJobsStorage to connect a function app to a storage account - Microsoft Community Hub
Note that the most critical part in order to succeed this is to uncheck the Add an Azure Files connection
box, when you create the function app, otherwise, this will not work (as explained in the documentation above)