Suppress empty multi-agent mode messages (#33862)

## What changed

- Treat an empty custom `multi_agent_mode_hint_text` as having no instructions to emit.
- Avoid adding an empty multi-agent mode message both on the initial turn and when the configured hint changes after resuming a session.

## Testing

- Update the empty-hint integration test to assert that no mode message is sent.
- Add resume coverage that verifies changing a custom hint to an empty string emits no update.

GitOrigin-RevId: 8033292115936fac2cf22f85141278595804ee61

codex-rs/core/src/context/multi_agent_mode_instructions.rs

@@ -12,8 +12,15 @@ pub(crate) struct MultiAgentModeInstructions {
 }
 
 impl MultiAgentModeInstructions {
-    pub(crate) fn new(multi_agent_mode: MultiAgentMode) -> Self {
-        Self { multi_agent_mode }
+    pub(crate) fn from_mode(multi_agent_mode: MultiAgentMode) -> Option<Self> {
+        if matches!(
+            &multi_agent_mode,
+            MultiAgentMode::Custom(hint_text) if hint_text.is_empty()
+        ) {
+            return None;
+        }
+
+        Some(Self { multi_agent_mode })
     }
 }
 

codex-rs/core/src/context_manager/updates.rs

@@ -95,9 +95,11 @@ fn build_multi_agent_mode_update_item(
     }
 
     match effective_multi_agent_mode {
-        Some(multi_agent_mode) => Some(MultiAgentModeInstructions::new(multi_agent_mode).render()),
+        Some(multi_agent_mode) => MultiAgentModeInstructions::from_mode(multi_agent_mode)
+            .map(|instructions| instructions.render()),
         None if previous.multi_agent_mode == Some(MultiAgentMode::Proactive) => {
-            Some(MultiAgentModeInstructions::new(MultiAgentMode::ExplicitRequestOnly).render())
+            MultiAgentModeInstructions::from_mode(MultiAgentMode::ExplicitRequestOnly)
+                .map(|instructions| instructions.render())
         }
         None => None,
     }

codex-rs/core/src/session/mod.rs

@@ -3471,10 +3471,10 @@ impl Session {
         {
             items.push(usage_hint_message);
         }
-        if let Some(multi_agent_mode) = multi_agents::effective_multi_agent_mode(turn_context) {
-            items.push(ContextualUserFragment::into(
-                MultiAgentModeInstructions::new(multi_agent_mode),
-            ));
+        if let Some(multi_agent_mode) = multi_agents::effective_multi_agent_mode(turn_context)
+            && let Some(instructions) = MultiAgentModeInstructions::from_mode(multi_agent_mode)
+        {
+            items.push(ContextualUserFragment::into(instructions));
         }
         if let Some(contextual_user_message) =
             crate::context_manager::updates::build_contextual_user_message(contextual_user_sections)