Laravel Pagination - changing the page makes my query vanish?

So I'm writing a page using Laravel that calls data from my database. First, lemme describe & show you my code, with the problem stated below it.

The database returns all its data in the form of a paginated table.

The user is given five fields and a submit box. Every field is optional, so they can be as specific as they like in their query. If no values at all are called, then it is a general search of the database.

My Controller's query looks like so:

 $postmen = DB::table('postmen')
   ->join('cats', 'postmen.cat_id', '=', 'cats.cat_id')
   ->join('reg_status', 'postmen.status_id', '=', 'reg_status.status_id')
   ->select('postmen.postmen_id', 'postmen.forename', 'postmen.surname',
    'cats.description AS catdesc', 'reg_status.description AS regdesc')
    ->where(function ($query) use ($request) {
      if (!empty($request->forename)) {
        $query->where('postmen.forename', $request->forename);
      }
      if (!empty($request->surname)) {
        $query->where('postmen.surname', $request->surname);
      }
      if (!empty($request->cat_id)) {
        $query->where('postmen.cat_id', $request->cat_id);
      }
      if (!empty($request->status_id)) {
        $query->where('postmen.status_id', $request->status_id);
      }
      if (!empty($request->postmen_id)) {
        $query->where('postmen.postmen_id', $request->postmen_id);
      }
    })
   ->paginate(10);

Now, the above code works, and returns for me a query with the values I want.

So, on the view side? I have a table that gives me the following:

    <form action="searchCriteria" method="get">
      @csrf
           <label for="forename">Forename: </label>
           <input type="text" name="forename">

           <label for="surname">Surname: </label>
           <input type="text" name="surname">

          <label for="cat_id">Cat: </label>
            <select name="cat_id">
              <option name="---" value=0>---</option>
              <option name="Black" value=1>Black Cat</option>
              <option name=”White” value=2>White Cat</option>
              <option name=”BlackWhite” value=3>Black and White Cat</option>
            </select>
    
          <label for="status">Status: </label>
            <select name="status_id">
              <option name="---" value=0>---</option>
              <option name="Injured" value=1>Injured</option>
              <option name="Working" value=2>Working</option>
              <option name="Holiday" value=3>Holiday</option> 
            </select>

           <label for="postman_id">Postman ID: </label>
           <input type="number" name="postman_id">
         
    
      <input type="submit" name="submit" value="Submit">

      <div class="form-group">
        <table id="postmanTable" data-page-length='5' cellspacing="0"
class="table table-bordered table-striped table-hover table-condensed"
role="grid">
        <!--Default table headers-->
          <thead class="thead-dark">
            <tr>
              <th scope="col">Postman ID:</th>
              <th scope="col">Name:</th>
              <th scope="col">Surname:</th>
              <th scope="col">Cat:</th>
              <th scope="col">Status:</th>
            </tr>
          </thead>
          <tbody>
    <!--Display all the data from the query-->  
            @if( !empty($postmen))
              @foreach ($postmen as $postman)
                <tr>
                  <td>{{$postman->postman_id}}
                    <input type='submit' name='submit' value={{$postman->postman_id}}></input>
                  </td>
                  <td>{{$postman->forename}}</td>
                  <td>{{$postman->surname}}</td>
                  @if( !empty($course))
                    <td>{{$course->description}}</td>
                  @else
                    <td>{{$postman->catdesc}}</td>
                  @endif
    
                  @if(!empty($status))
                    <td>{{$status->description}}</td>
                  @else
                    <td>{{$postman->regdesc}}</td>
                  @endif
                </tr>
              @endforeach
            @else
              <tr>
                <td>{{$postman->postman_id}} <input type='submit' name='submit' value={{$postman->postman_id}} ></input> </td>
                <td>{{$postman->forename}}</td>
                <td>{{$postman->surname}}</td>
                <td>{{$postman->catdesc}}</td>
                <td>{{$postman->regdesc}}</td>
              </tr>
            @endif


          </tbody>
        </table>
    
        @if(!empty($postmen) )
          @if ($postmen->hasMorePages())
            {{$postmen->links()}}
          @endif
        @else
          <h4>No postmen available under this query</h4>
        @endif
      </div>
    </form>

This also gives me the table I want, fully paginated, with paginated links to match.

So what is the problem?

It's when I try to go to a different page in the query other than the first. It thinks I should be clicking the Submit button thanks to my controller's validation (unshown) requiring the submit button be clicked.

And when I remove the validation so I can click the button as normal? Well the query completely changes, from a specific query to one that has no queries at all. If I query for all postmen with the forename "Tom", then look at page 2 of the results, I instead get every postman with any name at all, not just Tom. That shouldn't be the case.

Any advice? Such would be greatly appreciated if you could.