I could not find the respective REST API.
We have on-prem Azure DevOps 2020.
Fiddler does not help, there is no clear request there. The data seems to be embedded within HTML returned from the server.
EDIT 1
There is a very inefficient way - fetch all the builds with their timelines and filter those that have run or still running on the given agent. This is very resource greedy way to do it and I would not consider it as an answer.