Вам нужно назвать вывод как zip.
Ниже у меня работает скрипт Powershell:
Param(
[string]$collectionUrl = "https://vsrm.dev.azure.com/{organization}",
[string]$project = "0522TFVCScrum",
[string]$releaseid = "35",
[string]$filename = "D:\temp\ReleaseLogs_$releaseid.zip",
[string]$user = "username",
[string]$token = "password/PAT"
)
# Base64-encodes the Personal Access Token (PAT) appropriately
$base64AuthInfo = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(("{0}:{1}" -f $user,$token)))
$uri = "$collectionUrl/$project/_apis/Release/releases/$releaseid/logs"
Invoke-RestMethod -Uri $uri -Method Get -ContentType "application/zip" -Headers @{Authorization=("Basic {0}" -f $base64AuthInfo)} -OutFile $filename