How to add Promoted links to a web part zone via Powershell?

Try below code:

Add-PSSnapin "Microsoft.SharePoint.PowerShell"

$site = new-object Microsoft.SharePoint.SPSite("http://SharePointSite/subsite")
$spweb = $site.OpenWeb()


Write-Output $spweb.Title

$page = $spweb.GetFile("SitePages/Dummy.aspx")

Write-Output $page.Url

$wpm = $spweb.GetLimitedWebPartManager($page.Url,  [System.Web.UI.WebControls.WebParts.PersonalizationScope]::Shared)

$listTemplate = [Microsoft.SharePoint.SPListTemplateType]::170

$listName = "Prompt Links"

$list=$spweb.Lists[$listName]

Write-Output "debug"

$ViewID = $list.Views["All Promoted Links"].id

$ViewURL = $list.Views["All Promoted Links"].url

Write-Output $ViewID

$ListViewWebPart = New-Object Microsoft.SharePoint.WebPartPages.XsltListViewWebPart

$ListViewWebPart.FrameState="Normal" 

$ListViewWebPart.Title = "All Promoted Links"

$ListViewWebPart.ListName = ($list.ID).ToString("B").ToUpper()

$ListViewWebPart.ViewGuid = ($ViewID).ToString("B").ToUpper()

$ListViewWebPart.Direction="LeftToRight" 

$ListViewWebPart.ZoneID = "wpz"

$ListViewWebPart.PartOrder = 0

$ListViewWebPart.TitleUrl = $ViewURL 

$ListViewWebPart.DetailLink = $ViewURL 

$wpm.AddWebPart($ListViewWebPart, "", 0)