Azure support for .NET 4.8
According to my research, at the moment, Azure app service does not support .Net 4.8. Azure app service just supports up to .NET framework 4.7.2. For more details, please refer to the document.
According to the situation, I suggest you make your application as a Container in Visual Studio then deploy Container to Azure or deploy your application to Azure VM.
Update
Jeff Martinez says:
.NET Framework 4.8 support is coming to App Service.
Public Azure cloud deployment will begin in mid-late July 2020 completing by mid-September 2020. For our Sovereign clouds, deployment will begin by mid-late August 2020 and complete by early-October 2020.
As of late August 2019, updating Azure App Service to .Net 4.8 is planned.
Reference: https://feedback.azure.com/forums/169385-web-apps/suggestions/37566262-upgrade-app-service-with-net-4-8
There have been no updates to Azure App Service since 19 August 2019.
Reference: https://azure.microsoft.com/en-au/updates/?product=app-service
Late answer, but it has just been announced that deployment of .NET Framework 4.8 to Azure App Service will start in July 2020. See the GitHub issue.
Hope this helps anyone looking for an update on this.