Try
$yourVariable.Keys | % { $yourVariable[$_]['Next'] }
to get the value in "Next". Then you should "only" parse the content in "Next" to get the "referenceName" property.
I've tried to convert it via JSON-deserialisation (ConvertFrom-Json), but it failed, because the content is not a valid JSON serialized object, see (missing comma between properties!):
{"type": "AzureKeyVaultSecret" "store": {
// ValueCollection: I had a similar issue with a result of type ValueCollection in PowerShell, and this approach works in my case. In my case the object with type ValueCollection was returned by a CRM FetchXML query via the GetEntityDataByFetchSearch method. Based on the documentation, the return type should have been Dictionary<String,Dictionary<String,Object>.
Hope it helps...