Laravel + AJAX：分页链接不起作用

Question

I'm working with Laravel 5.8 and I am trying to set up pagination with live search via AJAX. I have configured it so that the pagination updates when the data is sent via a GET request due to the AJAX search. The only thing that isn't working is the link when I click to proceed to the next page.

When I click on a pagination link when the page is first loaded, the url looks like this http://localhost:8000/pagination?page=2 and it displays that page appropriately.

If I use my live search and click on a pagination link, the url looks like this http://localhost:8000/search?page=2 and doesn't display anything.

This is the AJAX in my pagination.blade.php file:

  $(function getResults(url) {
    $('#search').on('keyup',function(){
      $value=$(this).val();
      $.ajax({
        type: 'GET',
        url: '{{URL::to('search')}}',
        data:{ 'search':$value },
        success:function(data){
          console.log(data);
          $('tbody').empty();
          $('tbody').html(data);
        },
      error: function(err) {
        console.log(err);
      }
      });
    });

$(function() {
    $('body').on('click', '.pagination a', function(e) {
       e.preventDefault();
        var url = $(this).attr('href');
        getResults(url);
        window.history.pushState("", "", url);
        console.log(url);
    });
  });

This is my web.php file:

Route::get('/search', 'SearchController@search');
Route::resource('/pagination', 'SearchController');

My pagination is rendered in my SearchController.php file via $projects->render();

Let me know if you want me to include more code. I truly appreciate any help you can provide!

EDIT: Adding the SearchController.php code:

public function index(Request $request)
{
  $projects = Project::orderBy('name', 'asc')->paginate(5);

  if ($request->ajax()){
    return view('pagination_data', ['projects' => $projects])->render();
  }

  return view('pagination', compact('projects'));
}

public function search(Request $request)
{
  if($request->ajax())
{

  $projects=DB::table('projects')->where('name', 'LIKE', '%'.$request->search."%")->orwhere('description', 'LIKE', '%'.$request->search."%")->orderBy('name', 'asc')->paginate(5);

  $resultCount = DB::table('projects')->count();

  if($projects)
  {

    $output=$projects->render();

        foreach ($projects as $project) {
         $output.='<tr>'.
         '<td>'.
          '<a href="'. $project->link .'" target="_blank">'.
          $project->name.
          '</a>'.
         '</td>'.
         '<td>'.
          $project->description.
         '</td>'.
         '<td>'.
          $project->creator.
         '</td>'.
        '</tr>';
}

  return Response($output);
}

 else {
   $output='<tr class="alert alert-danger" role="alert">No projects found :(</tr>';

   return Response($output);
 }

}
}
}

EDIT: I fixed the http://localhost:8000/%7B%7B$project-%3Elink%7D%7D issue and I updated the code above.

EDIT, 6/1: I've narrowed down the issue further-- it seems like the pagination links are not updating after a live AJAX search is performed. http://localhost:8000/pagination?page=2 always refers to the original rows (before a search). I think the key to resolving this will be updating that initial link from the SearchController file. Each time a live search is performed, the SearchController code is pulled.