Remove manual home variable lookup

[kasperk81]

@ViktorHofer this is sdk part of

nuget NuGet/NuGet.Client@310f5d4
runtime dotnet/runtime@a7c6ff7

[ViktorHofer]

@dotnet/dotnet-cli PTAL

[kasperk81]

@baronfel and @marcpopMSFT i have waiting for months on this #44266 and really hope it makes it into .NET 10 preview. the current desync state is more problematic, so it feels like the options are either to take this change or revert the other two related ones in runtime and nuget. also, the scope of this change is limited to cases where the HOME variable isn’t set, so it avoids most usual use cases.

[ViktorHofer]

@kasperk81 we already snapped for .NET 10 Preview 1. Does this need to go into the first preview? If so, we would need to ask for approval.

[baronfel]

I don't think this is pressing enough to break glass for p1. It's important we get it into 10 previews period though.

[kasperk81]

it's targeting main branch so p1 is not affected.