Recursive function to transform JSON to "dot notation"

Question

I'm trying to get something working in Powershell where I can take a typical JSON file and restructure it so that it's represented in a sort of dot notation form.

As an input I'm reading in a JSON file. If, for example, the file looked something like:

{
    "Logging": {
        "MinLevel": {
            "Default": "Information",
            "Override": {
                "Host": "Warning"
            }
        },

        "Properties": {
            "ApplicationName": "My App"
        }
    },
    "ConnectionStrings": {
        "DefaultConnection": "string"
    }
}

... and from that, I'd like to end up with something flattened out but retaining the paths to the elements:

"Logging.MinLevel.Default" : "Information"
"Logging.MinLevel.Override.Host" : "Warning"
"Properties.ApplicationName" : "My App"

...

This is what I've been working towards and I think I'm sort of heading in the right direction but I've got pretty lost now. Here's my code:

function ConvertTo-DotNotation {
  param(
    [pscustomobject] $jsonObject,
    [string] $splitWith = ":",
    [string] $currentKey = ""
  )

  # Get all object members that we're interested in
  $jsonObjectProperties = $jsonObject | Get-Member -MemberType NoteProperty

  # Loop through each property and get the key and the corresponding value
  foreach ($property in $jsonObjectProperties) {
    $key = $property.Name
    $value = $jsonObject.$key
    $keyToPrepend = $key
    

    # Check if the value is an object itself
    if ($value -is [pscustomobject]) {
      Write-Host "val is an object, need to recurse"
      $nestedResult = ConvertTo-DotNotation -jsonObject $value -currentKey $keyToPrepend 
      # unsure what to set as result????

    } else {
      #unsure what to set as result ????
    }

    return $result
  }
}

$appsettingsjson = Get-Content -Path ./AppSettingsJSON/regular_json_file.json | ConvertFrom-Json
$flattenedAppsettings = ConvertTo-DotNotation -jsonObject $appsettingsjson

Any pointers on this? Alternative approaches also welcome if I'm making a meal of this...

Thanks