How can I enumerate a hashtable as key-value pairs / filter a hashtable by a collection of key values

You have some options here.

Enumerating through keys:

foreach ($key in $var.Keys) {
    $value = $var[$key]
    # or
    $value = $var.$key 
}

Enumerating key-value pairs (which you’ve discovered, but may not be using effectively):

foreach ($kvp in $var.GetEnumerator()) {
    $key = $kvp.Key
    $val = $kvp.Value
}