X-SP-End-User is what names that subject. Without the header your key is the organization, which owns the agent and reaches every thread on it. With the header you reach only the threads that person created; any other thread is a 404, exactly like a missing one.
GET /v1/agents/{agent_id} returns a threads array already filtered that way, which is how you list one person’s conversations. There is no separate endpoint for it, and you do not need one.
Create a thread
SendPOST /v1/agents/{agent_id}/threads.
The success response
The status is201. The thread is ready at once.
Errors
Read, change, and delete a thread
All three calls can return
503 service_unavailable with the message “This thread is temporarily unavailable” for a few seconds after a restart. Wait, then send the request again.