How to install azure devops extension from powershell script

I can't for the life of me understand what this api wan't from me ! I made a query to get the extensionId and publisherId from the cli. I connect with my tenantId because an admin PAT is not enough. Now he can't find it ?

function azLogin {
    param ( [string]$organization, [string]$tenant)

    az login --tenant $tenant
}


[string]$tenant = $args[0]
[string]$organization = $args[1]
[string]$extension = $args[2]
[string]$publisher = $args[3]

try {
    azLogin $organization $tenant

    $result = az devops extension search --search-query Timetracker | ConvertFrom-Json
    $extensionId = $result.extensionId
    $publisherId = $result.publisher.publisherId
    
    Write-Host $publisherId
    az devops extension install --extension-id $extensionId --publisher-id $publisherId

    if ($result.PSObject.Properties.Name -notcontains 'extensionId' -or $result.PSObject.Properties.Name -notcontains 'publisherId') {
        throw
    }
}
catch {
   Write-Error "##[ERROR] failed."
}

At this point it's supposed to install this the organisation but i get :

The requested extension 'ecbf0d3e-ca03-4972-88ad-edcd1cb4a69c.83b3c590-5cd3-495b-b401-b8b4ed6da230' doesn't exist.

How am i supposed to install an extension in my organisation using powershell and a pat only ?

Use azure devops service rest api may make things simple if you use PAT, API REFER

Below example shows how to install azure devops extension SonarQube (you can choose any extension you want), just copy and replace your own userName, PAT, orgName

function Get-AuthHeaders {
    [CmdletBinding()]
    param (
        [Parameter()]
        [string]$UserName,
        [string]$PersonalAccessToken
    )

    $basicAuth = ("{0}:{1}" -f $UserName, $PersonalAccessToken)
    $basicAuth = [System.Text.Encoding]::UTF8.GetBytes($basicAuth)
    $basicAuth = [System.Convert]::ToBase64String($basicAuth)
    $headers = @{Authorization = ("Basic {0}" -f $basicAuth) }
    return $headers
}
function Install-AdoExtension {
    [CmdletBinding()]
    param (
        [Parameter(Mandatory)]
        [string]$OrganizationName,
        [Parameter(Mandatory)]
        [string]$PublisherName,
        [Parameter(Mandatory)]
        [string]$ExtensionName,
        [Parameter(Mandatory)]
        [string]$Version,
        [Parameter(Mandatory)]
        [hashtable]$Headers
    )

    $uri = "https://extmgmt.dev.azure.com/{0}/_apis/extensionmanagement/installedextensionsbyname/{1}/{2}/{3}?api-version=7.2-preview.1" -f $OrganizationName, $PublisherName, $ExtensionName, $Version


    $response = Invoke-RestMethod -Uri $uri -Method 'Post' -ContentType 'application/json' -Headers $headers -Body $body

    return $response
}
function List-AdoExtension {

    [CmdletBinding()]
    param (
        [Parameter(Mandatory)]
        [string]$OrganizationName,
        [Parameter(Mandatory)]
        [hashtable]$Headers
    )
    $uri = "https://extmgmt.dev.azure.com/{0}/_apis/extensionmanagement/installedextensions?api-version=7.2-preview.1" -f $OrganizationName
    $response = Invoke-RestMethod -Uri $uri -Method 'Get' -Headers $headers

    return $response
}

##
$userName            = "wbaccesstoken20250228"
$personalAccessToken = "xxxxxxx"
$orgName = "yourOrgName"

$extensionName = 'SonarQube'
$publisherName = 'SonarSource'
$version = '5.19.2'

###
$headers = Get-AuthHeaders -UserName $userName -PersonalAccessToken $personalAccessToken

Install-AdoExtension -OrganizationName $orgName -PublisherName $publisherName -ExtensionName $extensionName -Version $version -Headers $headers

List-AdoExtension -OrganizationName $orgName -Headers $headers

my example result: