First, I see this question is tagged azure-web-app-service, but your question indicates you are not running the best practice method of running WordPress on App Service, which is by running the official Microsoft WordPress container image. Learn more about running WordPress on Azure using best practices here.

Second, to answer your question, I'm unable to tell if you're running an App Service with the PHP stack or as a virtual machine running in Azure. I'm thinking it must be a virtual machine.

Additionally, is there any option in the Azure Portal to modify the configuration so that I can apply chmod 755 and chmod 644?

If you truly are running an App Service, then your best option is to use Kudu. This will allow you to access SSH and have full access to the web app as you will be the root user. You will find 'Advanced Tools' on the left navigation under 'Developer Tools'. The URL will look similar to https://[your-app-service-name].scm.azurewebsites.net/. To access the new UI, which also provides a file editor for you, go to https://[your-app-service-name].scm.azurewebsites.net/newui.

By the sounds of you are already have SSH access. In which case it's hard to know what the issue could be without knowing:

• What user are you running as

• What is the error you are seeing when you fail to run the commands.