Recursive category Livewire 3.x and AlpineJS 3.x

I have created a recursive category display using Livewire 3.x and AlpineJS 3.x The categories are stored in the database. Everything is working except for the activeDropdown function. When I open a parent category and click on a child category inside it, the parent category does not remain open.

How can I solve this so that it stays open?

Thank you.

Source code:

resources\views\livewire\category-navigation.blade.php

<div x-data="sidebar" class="sidebar z-50 transition-all duration-300">
    <div class="bg-white">
        <ul class="p-4 py-0" x-data="{ activeDropdown: null }">
        @foreach ($categories as $category)
            @if ($category->children->count() > 0)
                <li class="nav-item">
                    <ul>
                        <li class="nav-item">
                            <button type="button" class="nav-link group"
                            :class="{ 'active': activeDropdown === '{{ $category->slug }}' }"
                                @click="activeDropdown === '{{ $category->slug }}' ? activeDropdown = null : activeDropdown = '{{ $category->slug }}'">
                                <div class="flex items-center">
                                    <span class="text-black">
                                        {{ $category->name }}
                                    </span>
                                </div>
                                <div class="" :class="{ '!rotate-90': activeDropdown === '{{ $category->slug }}' }">
                                    <svg width="16" height="16" viewBox="0 0 24 24" fill="none"
                                        xmlns="http://www.w3.org/2000/svg">
                                        <path d="M9 5L15 12L9 19" stroke="currentColor" stroke-width="1.5"
                                            stroke-linecap="round" stroke-linejoin="round" />
                                    </svg>
                                </div>
                            </button>
                            <ul x-cloak x-show="activeDropdown === '{{ $category->slug }}'" x-collapse class="sub-menu text-gray-500" @click.away="activeDropdown = null" @click.stop>
                                @foreach ($category->children as $child)
                                    @include('livewire.category-item', ['category' => $child])
                                @endforeach
                            </ul>
                        </li>
                    </ul>
                </li>
            @else
                <li class="nav-item">
                    <a href="{{ url($category->full_path) }}" wire:click.prevent="navigateToCategory('{{ $category->full_path }}')" class="nav-link group"
                        :class="{ 'active': '{{ request()->routeIs("products.byCategory") && request()->route("slug") == $category->slug ? "active" : "" }}'}">
                        <div class="flex items-center">
                            <span class="text-black">{{ $category->name }} ({{ $category->products()->count() }})</span>
                        </div>
                    </a>
                </li>
            @endif
        @endforeach
        </ul>
    </div>
</div>

resources\views\livewire\category-item.blade.php

@if ($category->children->count() > 0)
    <li x-data="{ subActive: null }">
        <button type="button"
            class="before:bg-gray-300 before:w-[5px] before:h-[5px] before:rounded before:mr-2 hover:bg-gray-100"
            :class="{ 'active': subActive === '{{ $category->slug }}' }"
            @click.stop="subActive === '{{ $category->id }}' ? subActive = null : subActive = '{{ $category->slug }}'">

            {{ $category->name }}

            <div class="ml-auto" :class="{ '!rotate-90': subActive === '{{ $category->slug }}' }">
                <svg width="16" height="16" viewBox="0 0 24 24" fill="none"
                    xmlns="http://www.w3.org/2000/svg">
                    <path d="M9 5L15 12L9 19" stroke="currentColor" stroke-width="1.5"
                        stroke-linecap="round" stroke-linejoin="round" />
                </svg>
            </div>
        </button>
        <ul class="sub-menu text-gray-500 ml-4" x-show="subActive === '{{ $category->slug }}'" x-collapse>
            @foreach ($category->children as $child)
                @include('livewire.category-item', ['category' => $child]) <!-- REKURZÍV hívás -->
            @endforeach
        </ul>
    </li>
@else
    <li>
        <a href="{{ url($category->full_path) }}" wire:click.prevent="navigateToCategory('{{ $category->full_path }}')">{{ $category->name }} ({{ $category->products()->count() }})</a>
    </li>
@endif

Js code:

document.addEventListener("alpine:init", () => {
    Alpine.data("sidebar", () => ({
        init() {
            const selector = document.querySelector('.sidebar ul a[href="' + window.location.href + '"]');
            if (selector) {
                selector.classList.add('active');
                const ul = selector.closest('ul.sub-menu');
                if (ul) {
                    let ele = ul.closest('li.menu').querySelectorAll('.nav-link');
                    if (ele) {
                        ele = ele[0];
                        setTimeout(() => {
                            ele.click();
                        });
                    }
                }
            }
        },
    }));
});