3.1.401 SDK fails to resolve correct available runtimes with 2.2.x

Describe the bug

I have a have a single target project with the following config:

<Project Sdk="Microsoft.NET.Sdk">
  <PropertyGroup>
    <TargetFramework>netcoreapp3.1</TargetFramework>
    <IsPackable>false</IsPackable>
  </PropertyGroup>
</Project>

The build machine has dotnet core SDK. 2.2.402 and 3.1.401 installed. When I attempt to build this project, the following error is emitted and the build fails:

##[error]C:\hostedtoolcache\windows\dotnet\sdk\2.2.402\Sdks\Microsoft.NET.Sdk\targets\Microsoft.NET.TargetFrameworkInference.targets(137,5): Error NETSDK1045: The current .NET SDK does not support targeting .NET Core 3.1.  Either target .NET Core 2.2 or lower, or use a version of the .NET SDK that supports .NET Core 3.1.

If I instead install SDKs 2.2.402 and 3.1.302 this error does not occur and the build succeeds.

To Reproduce

1. Install SDKs 2.2.402 and 3.1.401
2. Run msbuild.exe" "D:\a\1\s\MySolution.sln" /nologo /nr:false /dl:CentralLogger,"D:\a\_tasks\MSBuild_c6c4c611-aa2e-4a33-b606-5eaba2196824\1.166.2\ps_modules\MSBuildHelpers\Microsoft.TeamFoundation.DistributedTask.MSBuild.Logger.dll";"RootDetailId=|SolutionDir=D:\a\1\s"*ForwardingLogger,"D:\a\_tasks\MSBuild_c6c4c611-aa2e-4a33-b606-5eaba2196824\1.166.2\ps_modules\MSBuildHelpers\Microsoft.TeamFoundation.DistributedTask.MSBuild.Logger.dll" /p:DeployOnBuild=true /p:PublishProfile=WebDeployPackage /p:configuration="Release" /p:_MSDeployUserAgent="VSTS_4522ee20-b1c7-418b-b3de-2bf24bb4eccd_build_43_0"
3. Error (see above)

Expected Result

The build should succeed.

Additional information

This was discovered on Azure DevOps. Nothing changes between the two builds other changing the Use .NET Core task to target 3.1.302 instead of 3.1.x.

Was there a breaking change in the last patch build or is this a bug?

[wli3]

Sorry, we are closing to net5.0 release. Please expect a very long delay.

[wli3]

Are you saying that we can compile 2.2 dotnetcore web apps using only the 3.1 sdk?

Yes.

If so, does that mean the test step in our pipeline would then be the one to fail because it does need to run with the 2.2 runtime.

If you test, yes, it will fail to run. However I tried the following pipeline. If you install runtime and the SDK both in the same location. SDK will be able to find the runtime and run it.

- task: UseDotNet@2
  inputs:
    packageType: 'sdk'
    version: '3.1.402'
    installationPath: '$(Agent.ToolsDirectory)/dotnet1'
- task: UseDotNet@2
  inputs:
    packageType: 'runtime'
    version: '2.2.8'
    installationPath: '$(Agent.ToolsDirectory)/dotnet1'

dotnet --info result