feat(core): add watchdog runtime and prompts

Preserve the watchdog runtime and prompt behavior on top of the refreshed inbox branch and collapse the branch back to a single commit for easier future restacks.

Co-authored-by: Codex <noreply@openai.com>

codex-rs/app-server-protocol/src/protocol/thread_history.rs

@@ -2527,6 +2527,7 @@ mod tests {
                 prompt: "inspect the repo".into(),
                 model: "gpt-5.4-mini".into(),
                 reasoning_effort: codex_protocol::openai_models::ReasoningEffort::Medium,
+                spawn_mode: codex_protocol::protocol::AgentSpawnMode::Spawn,
                 status: AgentStatus::Running,
             }),
         ];