Better support for VSCode Icon folders in Solution Explorer

This is from @michaelstonis and migrated from https://github.com/dotnet/vscode-csharp/issues/6519

Is your feature request related to a problem? Please describe.

Not a problem at all, but a very minor nice to have. The Solution Explorer has good support for VSCode icons when displaying a file, but is inconsistent when displaying folders. VSCode icons appear to work on folders at the root of the solution, but they do not appear to work within a project.

Describe the solution you would like

I am not familiar with how the solution explorer applies the icons to folders, but it looks like it has its own set of rules for projects (for example, C# projects have a C# icon on them). If we could look at the VSCode icons as a fallback that would be great.

Applicable Scenarios

When opening a project with folder names that match VSCode icon configurations.

Describe alternatives you've considered

Not sure that there is a clear alternative.

Additional context

Below are screenshots showing differences between folders in the solution explorer and folder view.

Solution Explorer

Folder View

The issue names the Solution Explorer and folder view but provides no source files or tests. Start by locating the Solution Explorer folder-icon handling and compare it with the existing VSCode icon behavior for folders at the solution root. Done means matching VSCode-configured folder icons also appear within projects without breaking project-specific icons.