If anybody stumbles upon this same problem, here's how you can do it with powershell.
After creating the VSTS account, you need to log in and create a personal access token with Extensions (read and manage) in selected scopes.
$accountName = "yourAccount"
$personalAccessToken = "your-personal-access-token"
$uri = "https://" + $accountName + ".extmgmt.visualstudio.com/_apis/extensionmanagement/installedextensionsbyname/ms-appinsights/appinsightsreleaseannotations?api-version=5.0-preview.1"
Write-Host "Installing extension: Release Annotations for Azure Application Insights"
Invoke-RestMethod `
-Method Post `
-Uri $uri `
-ContentType application/json `
-Headers @{Authorization = 'Basic ' + [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(":$($personalAccessToken)")) }