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Search functionality should show the result with sorted cells not just highlight the cells with information. Just like filter.
I agree that search functionality can be significantly improved.
In the meantime, you might want to check out the Search Block — it’s a more advanced searching tool that DOES show a list of records as the result, and you can even specify which tables/fields to search.
HOWEVER — the Search Block also has significant limitations. For example, the results still can’t be sorted at all. And you have no ability to “mirror” the resulting list back into your main grid view, so you can’t get the same list of records in your grid. You also can’t export the records from the block, either. So essentially, the results just stand alone in the block, and you can’t do much with them except click on them one-at-a-time to expand an individual record.