On a side note, I don't understand why the IDE has options for
building multiple projects and multiple files in parallel, but not
multiple configurations.
Actually, in VS IDE, Batch Build UI has an option to config the configuration for projects.

But it can configure multiple configuration
, Platform
..... for projects but does not process build projects in parallel.
Suggestion
I suggest you could use a msbuild script to and then use MSBuild Command Line to run several projects with multiple platforms.
1) Create a file called test.proj
2) add these in it:
<Project xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
<ItemGroup>
<ProjectFile Include="C:\xxxx\ConsoleApplication1.vcxproj">
<Properties>Configuration=Release</Properties>
</ProjectFile>
<ProjectFile Include="C:\xxx\ConsoleApplication1.vcxproj">
<Properties>Configuration=Debug</Properties>
</ProjectFile>
<ProjectFile Include="C:\xxx\ConsoleApplication1.vcxproj">
<Properties>Configuration=xxx</Properties>
</ProjectFile>
.....
// add any configuration like this and remember to include the related vcxproj and even the same vcxproj has to be written for different configurations.
</ItemGroup>
<Target Name="ParelBuild">
<MSBuild Projects="@(ProjectFile)" BuildInParallel="true" Targets="Build" />
</Target>
</Project>
See this similar issue.
3) Note: Developer Command Prompt for VS2015
does not show the features of parallel build and I feel quite confused.
So to parallel build, I suggest you could download Build Tool for VS2019 which can be installed separately from VS2019 and supports lower versions of MSBuild 14.0. And I have tested successfully.
(the download link is under All Downloads-->Tools for Visual Studio 2019)
4) use this MSBuild command line to build:
msbuild test.proj -t:ParelBuild -v:normal -m:30
The effect is as follows:

Update 1
Build your own portfolio of projects at different times and you can try these:
<Project xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
<ItemGroup>
<ProjectFile Include="C:\xxxx\ConsoleApplication1.vcxproj">
<Properties>Configuration=Release</Properties>
</ProjectFile>
<ProjectFile Include="C:\xxx\ConsoleApplication1.vcxproj">
<Properties>Configuration=Debug</Properties>
</ProjectFile>
<ProjectFile Include="C:\xxx\ConsoleApplication1.vcxproj">
<Properties>Configuration=xxx</Properties>
</ProjectFile>
.....
// add any configuration like this and remember to include the related vcxproj and even the same vcxproj has to be written for different configurations.
</ItemGroup>
<ItemGroup>
<ProjectFile1 Include="C:\xxxx\ConsoleApplication1.vcxproj">
<Properties>Configuration=Release</Properties>
</ProjectFile1>
<ProjectFile1 Include="C:\xxx\xxx.sln">
<Properties>Configuration=Debug</Properties>
</ProjectFile1>
........
</ItemGroup>
<Target Name="ParelBuild1">
<MSBuild Projects="@(ProjectFile1)" BuildInParallel="true" Targets="Build" />
</Target>
</Project>
Then first build the ParelBuild target at one time:
msbuild test.proj -t:ParelBuild
After it, at another time, execute this:
msbuild test.proj -t:ParelBuild1
This allows you to execute combined projects in parallel at different points in time.