A judicious use of xargs, curl and grep would have done it in 1 line in Linux. I looked at your PowerShell code; that does look a bit complicated compared to what Linux offers.
Especially the fact that I was able to accomplish what I set out to do in a very reasonable amount of time.
$sites = @('https://www.google.com/', 'https://www.example.com/')
$searchString = 'oogle'
$sites | %{ if ((iwr $_).Content -like "*$searchString*") { "$_;OK" } else { "$_;NOT OK" } } > C:\temp\output.csv