WordPress, filter posts if a specific custom block is present on post

Question

I am wanting to filter WordPress posts that have a specific block present. I have the initial tagging done and can see which posts have the block I am searching for.

I tried using the query to do the actual filtering but got lost as the documentation I can find only filters using metadata from things like on page drop down menus. Can I add that type of metadata to a block?

// Add Column to admin post list
function custom_columns_list( $columns ) {

    $columns['blockBool'] = 'Block Present?';

    return $columns;
}
add_filter( 'manage_post_posts_columns', 'custom_columns_list' );


// check post if block is present
function blockColumn() {

//using a block from learn.wordpress
    if ( has_block( 'create-block/multi-columns' ) ) {
        // echo '<p>True</p>';
        $blockBool = "True";
        echo "$blockBool";
        
       } else {
        // echo '<p>False</p>';
        $blockBool = "False";
        echo "$blockBool";
        
       }

}
add_action( 'manage_posts_custom_column', 'blockColumn', 10, 2 );

// add filter drop down to post admin list
function blockCheckFilter( $post_type ) {

if ( $post_type === 'post' ) {
        $blockBool = filter_input( INPUT_GET, 'blockBool' );

        ?>
        <select name="blockBool">
            <option value="">Block Present?</option>
            <option value="True" <?php echo selected( 'True', $blockBool ); ?>>True</option>
            <option value="False" <?php echo selected( 'False', $blockBool ); ?>>False</option>
        </select>
        <?php
    }
}

add_action( 'restrict_manage_posts', 'blockCheckFilter', 10, 2 );

Here is where I got lost. I tried using $query->set to no positive results

//use query to filter block results?
function block_order_result( $query ) {

    $blockBool = filter_input( INPUT_GET, 'blockBool' );

    if ( is_admin() && ! empty( $blockBool ) ) {

        switch ( $blockBool ) {

            case 'True':
                echo "Show posts where blockBool is true";
                break;

            case 'False':
                echo "My brain hurts";
                break;

            default:
                // code...
                break;
        }
    }
}
add_action( 'pre_get_posts', 'block_order_result' );

function sort_column( $columns ) {

    $columns['blockBool'] = 'blockBool';
    return $columns;
}

add_filter( 'manage_edit-post_sortable_columns', 'sort_column' );

Here is what my current admin page looks like.