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/core/tests/suite/prompt_caching.rs

@@ -180,7 +180,8 @@ async fn prompt_tools_are_consistent_across_requests() -> anyhow::Result<()> {
         "spawn_agent",
         "send_input",
         "resume_agent",
-        "wait_agent",
+        "list_agents",
+        "wait",
         "close_agent",
     ]);
     let body0 = req1.single_request().body_json();