Install .NET Core command line. https://dot.net/core
Open a terminal to the directory containing this project.
dotnet watch msbuild /t:TestAndRun
The "TestAndRun" target in watch.proj will execute "dotnet test" on Test.csproj and then launch the website by calling "dotnet run" on Web.csproj.
Changing any *.cs file in Test/ or Web/, any *.csproj file, or watch.proj, will cause dotnet-watch to relaunch the "TestAndRun" target from watch.proj.