You won't be able to use =FILTER() within a table because by definition that cell with a formula in it has to be outside what it's filtering, that is, it has to be in another cell(s). Easy enough to do this while typing using an activeX text box and a linked cell. See attached where there's an activeX text box, linked to cell B10 whose value is used in a =FILTER function in cell D13. Of course, in this case it's just filtering the single column but it's very easy for that to apply to a whole table or a subset of the columns of a whole table.
Filtering the table itself is possible as you've said, with vba, but without vba there is the built-in functionality of the search box in the dropdowns of the headers of a table, this will visibly reduce the numbers of possibilities as you type (shown as checkboxes), but only for that column and within that dropdown's dialogue box. You'll only be able to see the full table result of that search-as-you-type when you finally
OK that dialogue box.
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