Display meta box dropdown (from custom post type) in the page post type

Here’s the updated meta box callback function. I’ve used get_posts() instead of WP_Query as get_posts() is more performant as well as easy to use in this case. And removed get_post_custom() as it’ll fetch all the custom metadata when you don’t need them. So, I’ve replaced that with get_post_meta(). Hope your dropdown will work as expected now.

I’d suggest you save post id (album id) instead of the title.

function meta_box_album_callback( $post ) {
    wp_nonce_field( 'my_meta_box_nonce', 'meta_box_nonce' );

    $mytheme_custom_select = get_post_meta( $post->ID, 'mytheme_custom_select', true );
    $albums = get_posts( array(
        'post_type'      => 'albums',
        'post_status'    => 'publish',
        'posts_per_page' => -1
    ) );
    ?>

    <p>
        <label for="mytheme_custom_select">Select album:</label><br>
        <select id="mytheme_custom_select" name="mytheme_custom_select">
            <option value="">Selecht an album...</option>
            <?php foreach ( $albums as $album ) : ?>
                <option value="<?php echo esc_attr( $album->post_title ); ?>" <?php selected( $mytheme_custom_select, esc_attr( $album->post_title ) ); ?>><?php echo esc_html( $album->post_title ); ?></option>
            <?php endforeach; ?>
        </select>
    </p>

    <?php
}

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