refactor: update cursor request handling and improve parent request management

- Changed `run_id` to `request_id` in `CursorParent` struct for clarity.
- Enhanced the `prepare` function to handle parent requests asynchronously, ensuring proper error handling for active runs.
- Updated database interactions to include `cursor_request_id` for better tracking of requests.
- Added tests to verify the behavior of reused cursor request IDs and their mapping to distinct executions.

server/tests/client_contract.rs

@@ -200,6 +200,7 @@ async fn prepared(store: &cursor_server::store::Store) -> PreparedRun {
     let root = store.ensure_conversation(&conversation_id).await.unwrap();
     PreparedRun {
         run_id: RunId::new("run"),
+        cursor_request_id: None,
         conversation_id,
         kind: RunKind::Root,
         model: ModelSpec::new("model"),