Custom MSBuild project that can be "run" from Visual Studio - visual-studio

Question

I created a custom MSBuild project that I can "build" from Visual Studio 2019, as described in https://stackoverflow.com/a/64917535/1536933. That is, I can select the Build menu item in VS and it runs my custom MSBuild task. Is there a way to do the same with "Run" - get VS to run my custom MSBuild task when I "Start" (or "Start without debugging") that project? I worked out that for the Build menu item to appear VS needs to see MSBuild targets named "Build" and "CoreCompile" - there is probably some equivalent for Start, but what?
The custom project file looks like this:
<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003" ToolsVersion="4.0">
<Import Project="$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props" Condition="Exists('$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props')" />
<PropertyGroup>
<Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
<SchemaVersion>2.0</SchemaVersion>
<ProjectGuid>(some guid)</ProjectGuid>
<ProjectHome>.</ProjectHome>
<ProjectTypeGuids>{3AF33F2E-1136-4D97-BBB7-1795711AC8B8};{9092AA53-FB77-4645-B42D-1CCCA6BD08BD}</ProjectTypeGuids>
</PropertyGroup>
<!-- These property groups can be empty, but need to be defined for VS -->
<PropertyGroup Condition=" '$(Configuration)' == 'Debug' ">
</PropertyGroup>
<PropertyGroup Condition=" '$(Configuration)' == 'Release' ">
</PropertyGroup>
<Import Project="My.Build.targets" />
<!-- Define empty standard MSBuild targets, since this project doesn't have them. Doing it this way allows My.Build.targets to also be used in a project that does define them. -->
<Target Name="Build" />
<Target Name="ReBuild" />
<Target Name="Clean" />
<!-- NOTE: a target named "CoreCompile" is needed for VS to display the Build menu item. -->
<Target Name="CoreCompile" />
<!-- Files shown in Visual Studio - adding and removing these in the UI works as expected -->
<ItemGroup>
<Content Include="myfile..." />
</ItemGroup>
</Project>
Note that it's not a C# project or C++ project or any other common type of project - VS treats its as a Node.js project due to the ProjectTypeGuids, but if I can get it working some other way, I'd be happy to.