This should work. I converted the date to unix time via strtotime.
foreach ($originalArray as $key => $part) {
$sort[$key] = strtotime($part['datetime']);
}
array_multisort($sort, SORT_DESC, $originalArray);
One-liner version would be using multiple array methods:
array_multisort(array_map('strtotime',array_column($originalArray,'datetime')),
SORT_DESC,
$originalArray);