How can you get Powershell to interact with elements on a webpage

Question

I am trying to write a Powershell script that will interact with elements of a webpage. To learn the concepts for the script, I am using Armorgames.com as the target url with my aim to use powershell to log into the site, then make a search of available games according to specified search terms, then export the results to a CSV. The attached code sample is what I currently have. But I'm having trouble understanding which parts of the webpage elements I'm searching for and how to input values into the available fields. I am also getting the error "Method invocation failed because [mshtml.HTMLDocumentClass] does not contain a method named 'getElementsById'" and I don't understand why

$ie = New-Object -ComObject "InternetExplorer.Application"
$requestUrl = "https://armorgames.com/"
$userId = "username-input";
$passwordId = "password-input"
$signIn = "act"

$ie.visible = $true
#ie.silent = $true
$ie.navigate($requestUrl)
while ($ie.busy) {
    Start-Sleep -Milliseconds 100
}
$doc = $ie.Document
$doc.getElementsById("input") | % {
    if ($_.id -ne $null){
        if ($_.id.Contains($signIn)) { $btn = $_ }
        if ($_.id.Contains($passwordId)) { $pwd = $_ }
        if ($_.id.Contains($userId)) { $user = $_ }
    }
}

$user.value = "ExampleUser"
$pwd.value = "MyPassord"

$btn.disabled = $false
$btn.click()
Write-Output $ie
Write-Output "doc is $doc"