custom search query database in child theme

The text input names don’t match the $_POST keys you are looping. Using [] in the input name attribute is for handling multiple inputs, not multiple keys.

Try replacing name="search[batch_no]" and name="search[rfid_chip_no]" with simply name="search_batch_no" and name="search_rfid_chip_no" and looping $_POST instead of $_POST["search"].

Also you need to check the conditions match, as only code and category are matched in your input processing, there is no sign of batch_no or rfid_chip_no, so I have no idea how it could be ‘working locally’ unless it is simply selecting all records locally because the query condition is ignored.