What is going wrong with web deployment from Visual Studio and App service?
All of a sudden VSTS default deployment mode became Run-From-Zip.
The solution is setting Select deployment method checkbox in VSTS deploy and be sure Web Deploy is selected.
To "unlock" the service you need to delete setting WEBSITE_RUN_FROM_PACKAGE from Application settings page in the Azure Portal - it is under 'Configuration'
I hade the same problem today with net core 2.2 and the solution was to remove setting "WEBSITE_RUN_FROM_PACKAGE" in azure appsettings
We got hit by this same issue - the file system becomes readonly when WEBSITE_RUN_FROM_PACKAGE=1. Azure App Service seems to be adding this app setting automatically during recent platform upgrades.
I do suggest using Run-From-Package over web deploy - but you can easily revert their forced updates by setting WEBSITE_RUN_FROM_PACKAGE=0. If you are on Azure DevOps - the latest version of App Service Deploy v4 supports Run-From-Package.