[codex] Migrate thread turns list to thread store (#19280)

- migrate `thread/turns/list` to ThreadStore. Uses ThreadStore for most
data now but merges in the in-memory state from thread manager
- keep v2 `thread/list` pathless-store friendly by converting
`StoredThread` directly to API `Thread`
- add regression coverage for pathless store history/listing

codex-rs/core/src/codex_thread.rs

@@ -31,6 +31,9 @@ use codex_protocol::protocol::ThreadMemoryMode;
 use codex_protocol::protocol::TokenUsageInfo;
 use codex_protocol::protocol::W3cTraceContext;
 use codex_protocol::user_input::UserInput;
+use codex_thread_store::StoredThreadHistory;
+use codex_thread_store::ThreadStoreError;
+use codex_thread_store::ThreadStoreResult;
 use codex_utils_absolute_path::AbsolutePathBuf;
 use rmcp::model::ReadResourceRequestParams;
 use std::collections::HashMap;
@@ -382,6 +385,20 @@ impl CodexThread {
             .await
     }
 
+    pub async fn load_history(
+        &self,
+        include_archived: bool,
+    ) -> ThreadStoreResult<StoredThreadHistory> {
+        let live_thread = self
+            .codex
+            .session
+            .live_thread_for_persistence("load history")
+            .map_err(|err| ThreadStoreError::Internal {
+                message: err.to_string(),
+            })?;
+        live_thread.load_history(include_archived).await
+    }
+
     pub fn state_db(&self) -> Option<StateDbHandle> {
         self.codex.state_db()
     }