Why does it say select the "ASP.NET Core" template when this is to build non asp.net core websites?
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ASP.NET core projects can still use .NET Framework for now.
I think this shouldn't have been closed. The doc page links to a repo
https://github.com/Microsoft/devops-project-samples/tree/master/dotnet/aspnet/webapp/Application
That's a non core MVC App.
This page Deploy a web app to Azure App Services was my entry point and how I got to this aforementioned page. It has this link:

I think it is wrong to state: Select the ASP.NET Core template, since the whole point of the page is to talk about how to build ASP.NET "traditional" apps on AzureDevOps. There's 0 to do with ASP.NET Core.
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ASP.NET core projects can still use .NET Framework for now.