If I understand correctly that the clicked checkboxes are already marked as checked after submitting the form, you could solve it as follows:
$selectedCategories = (isset($input->get->category)) ? $input->get->category : [];
<?php foreach ($pages->get(1104)->children() as $category) : ?>
<div class="flex items-center">
<input id="<?= $category->id; ?>" name="category[]" value="<?= $category->id; ?>" type="checkbox" class="text-gold-600 h-4 w-4 rounded border-brown-300 focus:ring-gold-500"<?php echo in_array($category->id, $selectedCategories) ? ' checked' : '' ?>/>
<label for="<?= $category->id; ?>" class="ml-3 text-brown-800"><?= $category->title; ?></label>
</div>
<?php endforeach; ?>
I hope this helps you!
