Hi Michael,
You may use below REST API to retrieve list as shown in your screenshot:
Web Apps - List
https://learn.microsoft.com/en-us/rest/api/appservice/web-apps/list
The user calling the api will need Microsoft.Web/sites/Read permission at subscription scope. In the Azure portal, if you navigate to your subscription, Access control (IAM) blade, click Add -- Add Custom role, you may create a custom role that only has the above permission.
Once the custom role has been created, use the same Access control (IAM) blade to assign the custom role to the user that will be calling the API.
Please click Accept Answer if the above was useful.
Thanks.
-TP