I cannot find any docs to handle this case, all I know is GitHub webhook but it seems to be for event notifications. I have a Spring Boot server, when workflow was triggered I need to send detailed logs to my server in real time (I think websocket can do that).
This isn't supported by GitHub Actions itself. Though there probably is an API you could call to get the data, since the website is able to live-view the log. That API isn't officially supported and is undocumented.
Simplest solution I can think of is to run something on the runner machine that monitors the log folder of the agent and streams that out in realtime. Either installed permanently on a self-hosted runner or installed very early on in the workflow of the hosted-runner.
Or to call the download logs API when the workflow run is finished.