Having said that, you might be able to do it using this filter:

https://searchandfilter.com/documentation/action-filter-reference/#filter-input-object

… where the PHP would first have to check to see if a search has been done, and then conditionally remove the numbers in brackets from the labels. But that might slow things down a little.

The general method to detect if a search has been made is this:

global $searchandfilter;
$sf_current_query = $searchandfilter->get(1234)->current_query();
if ((!$sf_current_query->is_filtered())&&($sf_current_query->get_search_term()=="")) {
  // code here to remove the counts
}

Replace the ID number with that of your form.

As the count is always in brackets, you could find the position of the last instance of ( in the string, and trim the string to that left most number of characters of the string (minus 1 I think, as there will be a space also).