Laravel 9 - Keep last insert of input value after submit

Hello, i'm reproducing an old site with Laravel and i have this behaviour to do

About the logic:

Let's say i have 3 controllers for OwnerInfo, StoreInfo, StatInfo. Each of them return an index view. The logic there is simple, just extract data from database and return to the view.

In my app.blade i'm using a "search form" partial component. In that input field the user inserts an ID that will be passed to the controller and used as the param for extract data. This component is visible for each mentioned views before. So basically it's one "search" for all views. I search for ID 5, with $request->input('id') i get it.

So i look for id 5 in OwnerInfo view and get all related data. Then when i want to go in StoreInfo view i need that the fields are already filled with data of ID 5.. And so for the other view. The problem is that after submit or page refresh the input value resets to null. I gave a look on session in laravel documentation and flash data, but i don't really understand on how to do it.

My code:

// search.blade.php

<nav class="navbar navbar-light">
    <form class="form-inline position-relative" method="GET">
    @method('GET')
      <input name="id" id="id" class="form-control shadow-none" type="number" placeholder="Code..."  value="{{ 	request()->input('id')}}">
      <button id="search-btn" type="submit" class="btn btn-light search-btn"><i class="fas fa-search"></i></button>
    </form>
</nav>

// app.blade.php

@include('partials.search') // search input

@yield('content') // any mentioned view

AnyController.php

public function index(Request $request)
{
	$id = $request->input('id');

	$data = DB::table('store_info')->where('id', $id)->get();

    return view('controller.index', compact('data'));
}