Ipad not recognize wired Headphone

It is worth making sure your iPad is fully up to date, or processing a full reset to see if that helps if you haven't done this already, but this sounds like a board level issue to me.

The iPad Pros are more similar to a MacBook in terms of their USB function they contain a proper USB controller, (that is also involved in charge function) that could have been damaged. They also contain a variant of the "Tristar" chip that is often damaged in iPhones or older iPads. In all possibility, one or both of these chips will need to be replaced to restore function.

Unfortunately it requires some advanced soldering skills to replace these, but it's a pretty common fault across the board. Image below is from the equivalent iPad Pro 11" but concept is the same.