Closing Web Messaging session via Genesys Cloud API

Hey everyone. We’re automating session cleanup using the Genesys Cloud API. I’m calling POST /api/v2/conversations/messaging/conversations/{conversationId}/participations/{participantId}/close to end the guest side. It returns a 204 No Content, which is good. But the conversation stays active in the queue for the agent. I’ve checked the Terraform state, and the routing config is standard. Is there another endpoint I need to hit to fully terminate the session on the backend?