The following list of fields types is possible to add to custom search (Studio > Forms > Search Fields):

'text', 'textarea', 'number', 'select', 'radio_set', 'checkbox_set', 'select_multiple', 'checkbox', 'switcher'

"Searchable fields for keyword search" setting is different setting which is for keyword search only, it's possible to add only text fields: 'text' and  'textarea'