Please suppress output new-item -type Directory -path "${TESTDRIVE}/$d" > $null.
Please use common formatting style:

 foreach ( $d in $dirnames ) {
    new-item -type Directory -path "${TESTDRIVE}/$d" > $null
}

sure, although this is slower than:
$null = New-Item -type Directory -path "${TESTDRIVE}/$d"

Should we use cmdlet? Maybe better .Net method to get current directory or -LiteralPath?

it really doesn't matter, does it?

I agree, maybe use

$result = & $powershell -c '([Environment]::CurrentDirectory)'

also, I want to check only the name, ason some systems, Environment.CurrentDirectory will include a symlink which is a problem because PS does not, I'm I need to call split-path, I can use this form just as well.

Since we are testing PowerShell, it would makes sense to use PowerShell i.e. the way Jim has written it rather then calling .NET. Why do you think it should be a .NET call? Is there some reason not to use native PowerShell capabilities?

My misunderstanding is that we use Directory.GetCurrentDirectory() in the code and Set-Location and Get-Item in the test - do we work with different current directories (first in .Net, second in FileSystem provider)?

(style) Maybe it's just my OCD, by why configuring providerContext inside try block rather than right after initialization?

I wanted the two operations to be visually close, putting the assignment in the block did that for me

We iterate over $dirname twice, once for new-item and once for generating test cases. Should be do it in a single loop?

sure

I agree, maybe use

$result = & $powershell -c '([Environment]::CurrentDirectory)'