How do I install an app from Windows Store using Powershell

store.rg-adguard.net is a GUI for generating direct download links to store apps. Peeking at the source of that page, we can piggyback off them to download the content directly, but using PackageFamilyName, rather than Name (in your example it would be Microsoft.HEVCVideoExtension_8wekyb3d8bbwe).

function Download-AppxPackage {
[CmdletBinding()]
param (
  [string]$PackageFamilyName,
  [string]$Path
)
   
  process {
    $WebResponse = Invoke-WebRequest -Method 'POST' -Uri 'https://store.rg-adguard.net/api/GetFiles' -Body "type=PackageFamilyName&url=$PackageFamilyName&ring=Retail" -ContentType 'application/x-www-form-urlencoded'
    $LinksMatch = $WebResponse.Links | where {$_ -like '*_x64*.appx*'} | Select-String -Pattern '(?<=a href=").+(?=" r)'
    $DownloadLinks = $LinksMatch.matches.value 

    for ($i = 1; $i -le $DownloadLinks.Count; $i++) {
      Invoke-WebRequest -Uri $DownloadLinks[$i-1] -OutFile "$Path\$PackageFamilyName($i).appx"   
    }
  }
}

This is limited to the x64 version, and the path must point to a folder. It will download the package and its dependencies and save them all as PackagefamilyName(n).appx

function Download-AppxPackage {
[CmdletBinding()]
param (
  [string]$Uri,
  [string]$Path = "."
)
   
  process {
    echo ""
    $StopWatch = [system.diagnostics.stopwatch]::startnew()
    $Path = (Resolve-Path $Path).Path
    #Get Urls to download
    Write-Host -ForegroundColor Yellow "Processing $Uri"
    $WebResponse = Invoke-WebRequest -UseBasicParsing -Method 'POST' -Uri 'https://store.rg-adguard.net/api/GetFiles' -Body "type=url&url=$Uri&ring=Retail" -ContentType 'application/x-www-form-urlencoded'
    $LinksMatch = ($WebResponse.Links | where {$_ -like '*.appx*'} | where {$_ -like '*_neutral_*' -or $_ -like "*_"+$env:PROCESSOR_ARCHITECTURE.Replace("AMD","X").Replace("IA","X")+"_*"} | Select-String -Pattern '(?<=a href=").+(?=" r)').matches.value
    $Files = ($WebResponse.Links | where {$_ -like '*.appx*'} | where {$_ -like '*_neutral_*' -or $_ -like "*_"+$env:PROCESSOR_ARCHITECTURE.Replace("AMD","X").Replace("IA","X")+"_*"} | where {$_ } | Select-String -Pattern '(?<=noreferrer">).+(?=</a>)').matches.value
    #Create array of links and filenames
    $DownloadLinks = @()
    for($i = 0;$i -lt $LinksMatch.Count; $i++){
        $Array += ,@($LinksMatch[$i],$Files[$i])
    }
    #Sort by filename descending
    $Array = $Array | sort-object @{Expression={$_[1]}; Descending=$True}
    $LastFile = "temp123"
    for($i = 0;$i -lt $LinksMatch.Count; $i++){
        $CurrentFile = $Array[$i][1]
        $CurrentUrl = $Array[$i][0]
        #Find first number index of current and last processed filename
        if ($CurrentFile -match "(?<number>\d)"){}
        $FileIndex = $CurrentFile.indexof($Matches.number)
        if ($LastFile -match "(?<number>\d)"){}
        $LastFileIndex = $LastFile.indexof($Matches.number)

        #If current filename product not equal to last filename product
        if (($CurrentFile.SubString(0,$FileIndex-1)) -ne ($LastFile.SubString(0,$LastFileIndex-1))) {
            #If file not already downloaded, add to the download queue
            if (-Not (Test-Path "$Path\$CurrentFile")) {
                "Downloading $Path\$CurrentFile"
                $FilePath = "$Path\$CurrentFile"
                $FileRequest = Invoke-WebRequest -Uri $CurrentUrl -UseBasicParsing #-Method Head
                [System.IO.File]::WriteAllBytes($FilePath, $FileRequest.content)
            }
        #Delete file outdated and already exist
        }elseif ((Test-Path "$Path\$CurrentFile")) {
            Remove-Item "$Path\$CurrentFile"
            "Removing $Path\$CurrentFile"
        }
        $LastFile = $CurrentFile
    }
    "Time to process: "+$StopWatch.ElapsedMilliseconds
  }
}


if (-Not (Test-Path "C:\Support\Store")) {
    Write-Host -ForegroundColor Green "Creating directory C:\Support\Store"
    New-Item -ItemType Directory -Force -Path "C:\Support\Store"
}

Download-AppxPackage "https://www.microsoft.com/p/snip-sketch/9mz95kl8mr0l" "C:\Support\Store"

Modified the script so that it delete old versions and only download latest.

Much thanks to Yorai Levi for the original script!