Specifically target older version of single .NET Standard API/namespace (Entity Framework Core)

You seem to be mixing up some things there:

• The .NET Core SDK mostly determines the tooling that is available to you. Unless you have a good reason, you should always run the latest SDK. So you should use the current version 2.1.300 of the SDK. The SDK version has no direct impact on what runtime you will be using.
• If you want to run an ASP.NET Core application on version 2.1 on .NET Core, then you will have to use the netcoreapp2.1 target framework.
• Obviously, you will have to use the Microsoft.AspNetCore.* packages with version 2.1.
• If you want to use Entity Framework Core with version 2.0.x, then you need to explicitly reference that. Note that you cannot use the shared framework reference Microsoft.AspNetCore.App in that case.

So a project that uses ASP.NET Core 2.1 on .NET Core 2.1, using Entity Framework 2.0 with the Pomelo MySQL provider could look like this:

<Project Sdk="Microsoft.NET.Sdk.Web">

    <PropertyGroup>
        <TargetFramework>netcoreapp2.1</TargetFramework>
    </PropertyGroup>

    <ItemGroup>
        <PackageReference Include="Microsoft.AspNetCore" Version="2.1.0" />
        <PackageReference Include="Microsoft.AspNetCore.Mvc" Version="2.1.0" />
        <PackageReference Include="Microsoft.EntityFrameworkCore" Version="2.0.3" />
        <PackageReference Include="Pomelo.EntityFrameworkCore.MySql" Version="2.0.1" />
    </ItemGroup>

</Project>

If you are not trying to do this within an ASP.NET Core web project but in a library project instead, then you are targetting netstandard2.0. In that case, you just need to import the proper packages directly:

<Project Sdk="Microsoft.NET.Sdk">

    <PropertyGroup>
        <TargetFramework>netstandard2.0</TargetFramework>
    </PropertyGroup>

    <ItemGroup>
        <PackageReference Include="Microsoft.EntityFrameworkCore" Version="2.0.3" />
        <PackageReference Include="Pomelo.EntityFrameworkCore.MySql" Version="2.0.1" />
    </ItemGroup>

</Project>

Note that Entity Framework Core is not included in the .NET Standard, it is merely targetting it which means that it builds on top of the standard; just like your library project.

If you want to consume your library project from within an ASP.NET Core 2.1 application, then the restriction mentioned above will still apply: You cannot use the Microsoft.AspNetCore.App shared framework reference, since that will cause version conflicts.