Search functionality is not working in Livewire Laravel

I don't understand why is it not working i neither see any errors nor any progress. Somebody please help what i am missing in my code. I already put @livewireStyles in head and @livewireScripts in script section but search functionality is not working..

<?php

namespace App\Livewire;

use App\Models\Booking;
use Livewire\Component;

class SearchUsers extends Component
{
    public $searchTerm;
    public $bookings;
    
    public function render()
    {
        $searchTerm = '%' . $this->searchTerm . '%';
        $this->bookings = Booking::where('pickup', 'like', $searchTerm)->get();

        return view('livewire.search-users');
    }
}
<input wire:model="searchTerm" type="text" placeholder="Search users..">
@php($sl = 1)
                            @forelse($bookings as $booking)
                                <tr>
                                    <td>{{$sl++}}</td>
                                    <td>{{$booking->user->name}}</td>
                                    <td>{{$booking->icabbi_trip_id}}</td>
                                    <td>{{$booking->date}}</td>
                                    <td>{{ Carbon\Carbon::createFromFormat('H:i:s', $booking->time)->format('h:i A') }}</td>
                                    <td>{{$booking->pickup}}</td>
                                    <td>{{$booking->destination}}</td>
                                    <td>{{$booking->seats}}</td>
                                    <td>{{str_replace(' ', '-', ucwords(str_replace('-', ' ', strtolower($booking->type))))}}</td>
                                    <td>{{$booking->status}}</td>
                                    <td>{{Carbon\Carbon::parse($booking->updated_at)->format('h:i A')}}</td>
                                    <td>{{$booking->cancellation_reason}}</td>
                                </tr>
                            @empty
                                <tr>
                                    <td>No bookings available</td>
                                </tr>
                            @endforelse