There are two ways to do searches in Cross Sell: Quick Search (default) & Advanced Search. Please read below to know when to use each.
Quick Search (default): useful for searching by terms. Terms being defined as title, sku, tags, vendor, etc.
Can not be used to search for unpublished items.
Advanced Search: useful for searching by exact title only, BUT you can filter by collection, product type, vendor, published/unpublished state and items with or without Handpicked Cross sells.
You can also switch back to Quick Search when needed, but this will reset the search.