Add occurrence search for paginated threads (#33907)

## What changed

- Add the experimental `thread/searchOccurrences` app-server method for case-insensitive literal search across visible user messages and final assistant messages without replaying the thread.
- Return paginated snippets with UTF-16 match ranges and `thread/turns/list` cursors for navigating to each matching turn.
- Index persisted item types to efficiently select searchable messages from paginated thread history.

## Testing

- Add an app-server integration test covering pagination, steering messages, final-answer selection, Markdown normalization, and UTF-16 offsets.

GitOrigin-RevId: e80160e0f83eb4e5db8de862307085093bee362b

codex-rs/thread-store/src/local/mod.rs

@@ -39,10 +39,12 @@ use crate::LoadThreadHistoryParams;
 use crate::ReadThreadByRolloutPathParams;
 use crate::ReadThreadParams;
 use crate::ResumeThreadParams;
+use crate::SearchThreadOccurrencesParams;
 use crate::SearchThreadsParams;
 use crate::StoredModelContext;
 use crate::StoredThread;
 use crate::StoredThreadHistory;
+use crate::ThreadOccurrenceSearchPage;
 use crate::ThreadPage;
 use crate::ThreadSearchPage;
 use crate::ThreadStore;
@@ -278,6 +280,14 @@ impl LocalThreadStore {
     pub async fn list_items(&self, params: ListItemsParams) -> ThreadStoreResult<ItemPage> {
         thread_history::list_items(self, params).await
     }
+
+    /// Searches projection-backed visible messages within one paginated thread.
+    pub async fn search_thread_occurrences(
+        &self,
+        params: SearchThreadOccurrencesParams,
+    ) -> ThreadStoreResult<ThreadOccurrenceSearchPage> {
+        thread_history::search_thread_occurrences(self, params).await
+    }
 }
 
 impl ThreadStore for LocalThreadStore {
@@ -363,6 +373,13 @@ impl ThreadStore for LocalThreadStore {
         Box::pin(async move { search_threads::search_threads(self, params).await })
     }
 
+    fn search_thread_occurrences(
+        &self,
+        params: SearchThreadOccurrencesParams,
+    ) -> ThreadStoreFuture<'_, ThreadOccurrenceSearchPage> {
+        Box::pin(LocalThreadStore::search_thread_occurrences(self, params))
+    }
+
     fn update_thread_metadata(
         &self,
         params: UpdateThreadMetadataParams,