feat: persist and restore codex app's tools after search (#11780)

### What changed
1. Removed per-turn MCP selection reset in `core/src/tasks/mod.rs`.
2. Added `SessionState::set_mcp_tool_selection(Vec<String>)` in
`core/src/state/session.rs` for authoritative restore behavior (deduped,
order-preserving, empty clears).
3. Added rollout parsing in `core/src/codex.rs` to recover
`active_selected_tools` from prior `search_tool_bm25` outputs:
   - tracks matching `call_id`s
   - parses function output text JSON
   - extracts `active_selected_tools`
   - latest valid payload wins
   - malformed/non-matching payloads are ignored
4. Applied restore logic to resumed and forked startup paths in
`core/src/codex.rs`.
5. Updated instruction text to session/thread scope in
`core/templates/search_tool/tool_description.md`.
6. Expanded tests in `core/tests/suite/search_tool.rs`, plus unit
coverage in:
   - `core/src/codex.rs`
   - `core/src/state/session.rs`

### Behavior after change
1. Search activates matched tools.
2. Additional searches union into active selection.
3. Selection survives new turns in the same thread.
4. Resume/fork restores selection from rollout history.
5. Separate threads do not inherit selection unless forked.

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

@@ -170,6 +170,27 @@ impl SessionState {
         merged
     }
 
+    pub(crate) fn set_mcp_tool_selection(&mut self, tool_names: Vec<String>) {
+        if tool_names.is_empty() {
+            self.active_mcp_tool_selection = None;
+            return;
+        }
+
+        let mut selected = Vec::new();
+        let mut seen = HashSet::new();
+        for tool_name in tool_names {
+            if seen.insert(tool_name.clone()) {
+                selected.push(tool_name);
+            }
+        }
+
+        self.active_mcp_tool_selection = if selected.is_empty() {
+            None
+        } else {
+            Some(selected)
+        };
+    }
+
     pub(crate) fn get_mcp_tool_selection(&self) -> Option<Vec<String>> {
         self.active_mcp_tool_selection.clone()
     }
@@ -293,6 +314,40 @@ mod tests {
         assert_eq!(state.get_mcp_tool_selection(), None);
     }
 
+    #[tokio::test]
+    async fn set_mcp_tool_selection_deduplicates_and_preserves_order() {
+        let session_configuration = make_session_configuration_for_tests().await;
+        let mut state = SessionState::new(session_configuration);
+        state.merge_mcp_tool_selection(vec!["mcp__rmcp__old".to_string()]);
+
+        state.set_mcp_tool_selection(vec![
+            "mcp__rmcp__echo".to_string(),
+            "mcp__rmcp__image".to_string(),
+            "mcp__rmcp__echo".to_string(),
+            "mcp__rmcp__search".to_string(),
+        ]);
+
+        assert_eq!(
+            state.get_mcp_tool_selection(),
+            Some(vec![
+                "mcp__rmcp__echo".to_string(),
+                "mcp__rmcp__image".to_string(),
+                "mcp__rmcp__search".to_string(),
+            ])
+        );
+    }
+
+    #[tokio::test]
+    async fn set_mcp_tool_selection_empty_input_clears_selection() {
+        let session_configuration = make_session_configuration_for_tests().await;
+        let mut state = SessionState::new(session_configuration);
+        state.merge_mcp_tool_selection(vec!["mcp__rmcp__echo".to_string()]);
+
+        state.set_mcp_tool_selection(Vec::new());
+
+        assert_eq!(state.get_mcp_tool_selection(), None);
+    }
+
     #[tokio::test]
     // Verifies connector merging deduplicates repeated IDs.
     async fn merge_connector_selection_deduplicates_entries() {