This section could probably do with a lot more editorial attention, but
for now this is all there is in terms of documentation. The field is
already returned by Synapse:
https://github.com/element-hq/synapse/blob/4587decd678300217969f1d2f69b226421a33ced/synapse/handlers/admin.py#L150

`last_seen_ts` was introduced in
https://github.com/matrix-org/synapse/pull/16218