How to get the Gallery form/section just like in Gutenberg block?

wp.media is the JavaScript API WordPress uses to display the media library modal.

You can use it yourself by enqueueing a custom JS script on your admin page:

wp_enqueue_script('media-upload');
wp_enqueue_media();
wp_enqueue_script(
    'pb-admin-script',
    'admin.js',
    array(
        'jquery',
    )
);

Then work with it like this:

HTML:

<button class="upload_image_button button button-primary">
    <?php _e('Upload Image', 'pb'); ?>
</button>
<img src="" id="image-preview" style="display: none"/>

JS:

jQuery(document).ready(function($) {
    $(document).on('click', '.upload_image_button', function(event) {
        event.preventDefault();

        var imgPrev = $('#image-preview');

        var file_frame = wp.media.frames.file_frame = wp.media({
            title: 'Select or upload image',
            library: {
                type: 'image'
            },
            button: {
                text: 'Select'
            },
            multiple: false,
        });

        file_frame.on('select', function() {
            var attachment = file_frame.state().get('selection').first().toJSON();

            imgPrev.src = attachment.url;
            imgPrev.style.removeProperty('display');
        });

        file_frame.open();
    });

});