Yeah! I've found the solution!
There is a request code example:

$.ajax({ url: 'https://food-tracker.ru/foods', type: 'POST', dataType: 'JSON', data: {term: 'rjk'}, success: function (data) {console.log(data);} });

And there was server code:

protected function returnJSON($data) { header('text/html; charset=utf-8'); echo json_encode($data); die(0); }

The solution is to change line header('text/html; charset=utf-8'); to header('Content-type: application/json; charset=utf-8');

So, right working code is:

protected function returnJSON($data) { header('Content-type: application/json; charset=utf-8'); echo json_encode($data); die(0); }

Thanks for your attention!

P.S. But one question i still have: why was it working fine before, and brokes when just hosting changed?