How can I convert a PowerShell custom object to a valid JSON file

Question

I'm trying to add the length of an UTF-8 string as a new value pair to the following JSON file:

{
    "uuid": "6f74b1ba-0d7c-4c85-955b-2a4309f0e8df",
    "records": {
        "record1": [{
                "locale": "en_US",
                "category": "alpha",
                "contents": "My hovercraft is full of eels"
            }
        ],
        "record2": [{
                "locale": "cs_CZ",
                "category": "alpha",
                "contents": "Moje vznášedlo je plné úhořů"
            }
        ],
        "record3": [{
                "locale": "es_ES",
                "category": "alpha",
                "contents": "Mi aerodeslizador está lleno de anguilas"
            }
        ]
    }
}

using the following code:

$infile = "C:\Temp\input.json"
$outfile = "C:\Temp\output.json"

$json = Get-Content $infile -Encoding UTF8 | ConvertFrom-Json
$records = $json.records

$records.PSObject.Properties | ForEach-Object {
    $length = $_.Value.contents.length
    $_.Value | Add-Member -Type NoteProperty -Name 'length' -Value $length
}

$json | ConvertTo-Json | Out-File $outfile -Encoding UTF8

The code seems to work, but when I output the file I get this, which looks like PowerShell code, not a JSON file.

{
    "uuid":  "6f74b1ba-0d7c-4c85-955b-2a4309f0e8df",
    "records":  {
                    "record1":  [
                                    "@{locale=en_US; category=alpha; contents=My hovercraft is full of eels; length=29}"
                                ],
                    "record2":  [
                                    "@{locale=cs_CZ; category=alpha; contents=Moje vznášedlo je plné úhořů; length=28}"
                                ],
                    "record3":  [
                                    "@{locale=es_ES; category=alpha; contents=Mi aerodeslizador está lleno de anguilas; length=40}"
                                ]
                }
}

But I want to get this:

{
    "uuid": "6f74b1ba-0d7c-4c85-955b-2a4309f0e8df",
    "records": {
        "record1": [{
                "locale": "en_US",
                "category": "alpha",
                "contents": "My hovercraft is full of eels",
                "length": 29
            }
        ],
        "record2": [{
                "locale": "cs_CZ",
                "category": "alpha",
                "contents": "Moje vznášedlo je plné úhořů",
                "length": 28
            }
        ],
        "record3": [{
                "locale": "es_ES",
                "category": "alpha",
                "contents": "Mi aerodeslizador está lleno de anguilas",
                "length": 40
            }
        ]
    }
}

What part of my code do I need to change?

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