I wanted to throw a PowerShell download option on the pile in case anyone else comes across this. I have several offline scenarios and I run this in a loop to download and update all of the extensions I use offline.
$page = Invoke-WebRequest -Uri 'https://marketplace.visualstudio.com/items?itemName=ms-vscode.PowerShell'
$details = ( $page.Scripts | ? {$_.class -eq 'vss-extension'}).innerHTML | Convertfrom-Json
$extensionName = $details.extensionName
$publisher = $details.publisher.publisherName
$version = $details.versions.version
Invoke-WebRequest -uri "$($details.versions.fallbackAssetUri)/Microsoft.VisualStudio.Services.VSIXPackage" `
-OutFile "C:\Scripts\extensions\$publisher.$extensionName.$version.VSIX"