how to open the azure devops signin screen from powershell?

I'm writing a powershell script to rotate my PAT in my devbox. Here's what I've done:

PS> .\Rotate-Pat.ps1

Here's the code in Check-PatValidity.ps1:

$env:PAT | az devops login --organization "https://dev.azure.com/$organization"

    $body = @{
        displayName = $organization
        scope = "vso.build vso.code_full vso.tokens vso.profile"
        validTo = (Get-Date).AddDays(7).ToString("yyyy-MM-ddTHH:mm:ssZ")
        allOrgs = $false
    } | ConvertTo-Json

    $response = Invoke-RestMethod -Uri "https://vssps.dev.azure.com/$organization/_apis/tokens/pats?api-version=7.1-preview.1" -Headers $headers -Method Post -Body $body -ContentType "application/json"
    
    $prettyJson = $response | ConvertTo-Json -Depth 2
    $prettyJson | Out-file $env:USERPROFILE\Downloads\patgenoutput.json -Encoding UTF8

    if ($response) {
        $newPat = $response.patToken.token
        Write-Output "New PAT: $newPat"
    }

Here's what I see as output (which is exactly the same as patgenoutput.json):

Looks like the html of Azure DevOps Login screen.

Questions:

1. Am I on the right track? If not, please point me in the right direction.
2. How to make the Azure DevOps login as an interactive session and get the access token to generate the PAT?

Alternatively, make use of below modified script that asks user to login interactively and generates bearer token to call Azure DevOps API for PAT creation:

$organization = "demodevOps25"

Write-Output "Logging into Azure..."
$loginOutput = az login --tenant "xxxxxxxxx.onmicrosoft.com" --only-show-errors

try {
    $token = az account get-access-token --resource "499b84ac-1321-427f-aa17-267ca6975798" | ConvertFrom-Json
} catch {
    Write-Error "Failed to retrieve access token. Please check your Azure login status."
    exit
}

$headers = @{
    Authorization = "Bearer $($token.accessToken)"
    'Content-Type' = 'application/json'
}

$body = @(
    @{
        displayName = $organization
        scope = "vso.build vso.code_full vso.tokens vso.profile"
        validTo = (Get-Date).AddDays(7).ToString("yyyy-MM-ddTHH:mm:ssZ")
        allOrgs = $false
    }
) | ConvertTo-Json

$response = Invoke-RestMethod -Uri "https://vssps.dev.azure.com/$organization/_apis/tokens/pats?api-version=7.1-preview.1" `
                              -Headers $headers `
                              -Method Post `
                              -Body $body `
                              -ContentType "application/json"

if ($response -and $response.patToken) {
    $newPat = $response.patToken.token
    Write-Output "New PAT generated: $newPat"
    $outputPath = Join-Path $env:USERPROFILE "Downloads\patgenoutput.json"
    $response | ConvertTo-Json -Depth 3 | Out-File $outputPath -Encoding UTF8
    Write-Output "PAT details saved to: $outputPath"
} else {
    Write-Error "Failed to generate PAT. Check the request body and API version."
}

Output:

To confirm that, I checked the saved file where new PAT details displayed successfully as below:

Azure DevOps Portal: