[https://docs.microsoft.com/en-us/rest/api/azure/devops/distributedtask/pools/get%20agent%20pools?view=azure-devops-rest-6.0]
The above document indicates that Deployment pools should be included. Unfortunately, they are not returned (although all of the "automation" pools are.
So how does one programmatically list, get (by id) and create/update these pools????
UPDATE....
Capturing network traces while viewing /_settings/deploymentpools?view=pool
has revealed that there is a ReST call to _apis/distributedtask/deploymentPools
which displays the proper information. HOWEVER, continued searching of docs.microsoft.com does not provide any information on this rest call.
UPDATE 2: Returned (sanitized) JSON for call Matt recommended:
JSON from _apis/distributedtask/deploymentPools/deploymentPoolsSummary?expands=2&api-version=6.1-preview.1
As can be seen, the two are not equivalent and so far only the call reverse engineered from the UI shows the same information set (including 2 needed fields related to online and offline counts)