We do not have a dedicated event that will fire after the search action. You can use the render.mdb.datatable event for this.

You can also do the whole thing inside the search function. If I understand correctly, inside the search function you send a query to the API and you have to wait for data? So you can do something like this:

document.getElementById('datatable-search-input').addEventListener('input', (e) => {
  // show loader

  fetch('server_url')
  .then((response) => response.json())
  .then((data) => {
    // update datatable data
    // hide loader
  });
});