There doesn't seem to be a single source in the API to get the equivalent view. See this github issue here.
Following the conversation in github, once you have a handle on what environments exist in your release definitions. You can do it by making multiple calls to the deployments endpoint.
PowerShell example:
param (
[string]$token,
[string]$collection,
[string]$projectName
)
$base64AuthInfo = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(("{0}:{1}" -f $user, $token)))
$response = Invoke-RestMethod "https://vsrm.dev.azure.com/$collection/$projectName/_apis/release/definitions?`$expand=Environments&`$top=100&api-version=5.1" -Method 'GET' -Headers @{Authorization = ("Basic {0}" -f $base64AuthInfo)}
foreach ($releaseDefinition in $response.value){
write-host $releaseDefinition.name
write-host "--------------------------------------------------"
foreach ($environment in $releaseDefinition.environments){
write-host $environment.name
$definitionEnvironmentId = $environment.id
$response = Invoke-RestMethod "https://vsrm.dev.azure.com/$collection/$projectName/_apis/release/deployments?api-version=5.0&deploymentStatus=succeeded&latestAttemptsOnly=true&definitionEnvironmentId=$definitionEnvironmentId&`$top=1" -Method 'GET' -Headers @{Authorization = ("Basic {0}" -f $base64AuthInfo)}
write-host $response.value[0].release.name $response.value[0].deploymentStatus $response.value[0].completedOn
}
write-host "--------------------------------------------------"
}