Is there any way to force a Gutenberg block to be on every page of a post type?

I tried to add a template on my page and it does almost what I need, but I can still remove my default blocks.

The closest I’ve come is this:

function ckt_mina_init_required_block()
{
    // create a new page template (pages only)
    $page_type_object = get_post_type_object('page');
    $page_type_object->template = [
        [
            'core/group',
            [],
            [
                // add a paragraph block for the page summary
                [
                    'core/paragraph',
                    [
                        'placeholder' => __('Excerpt'),
                    ],
                ],
                [
                    'core/image',
                    [],
                ],
            ],
        ],
    ];
    $page_type_object->template_lock = 'all';
}

add_action('init', 'ckt_mina_init_required_block');

This will create a new page template and use it on every new page. The 2 blocks “paragraph” and “image” will be present in the first group.

But I cannot add any other block to my page.

Or, I can remove the template_lock = 'all', but then, my blocks can be removed during the page creation.

Any idea on how I might achieve to have 2 fixed blocks at the beginning of my Gutenberg area?