Function process_with_agent_with_experience_id 

pub async fn process_with_agent_with_experience_id(
    state: &AppState,
    context: AgentRequestContext<'_>,
    override_prompt: Option<&str>,
    image_data: Option<(String, String)>,
    experience_run_id: String,
) -> Result<String>

Run the shared loop with a caller-owned durable experience id. This lets supervisors close the record even if they time out and drop the future.