Function run_search_impl 

pub async fn run_search_impl(
    ctx: &CoreCtx,
    user_id: u64,
    params: &SearchParams,
    api_query: &str,
    started: Instant,
) -> Result<(i64, Vec<SearchResult>)>

The actual search execution (with cache + searchlog). Extracted so the intent fallback can reuse the same cache/analytics path.