Meta Box

The workaround

/**
 * Plugin Name: Meta Box and WP Grid Builder relationship compatibility
 * Description: Automatically restores registered Meta Box relationship sources in copied WP Grid Builder post queries, including AND/OR combinations.
 * Version: 0.2.0
 */
defined('ABSPATH') || exit;

final class MB_WPGB_Relationship_Compat {
    /** Repair only normalized clauses belonging to registered relationships. */
    public static function restore_clause($args) {
        if (!is_array($args) || !is_string($args['id'] ?? null)) return $args;
        // Preserve fresh arguments, including explicitly supplied source IDs.
        if (isset($args['from']) || isset($args['to'])) return $args;
        $direction = $args['direction'] ?? '';
        if (!in_array($direction, ['from', 'to'], true) || !isset($args['items']) || !is_array($args['items'])) return $args;
        $relationship = MB_Relationships_API::get_relationship($args['id']);
        if (!$relationship || ($args['id_field'] ?? null) !== $relationship->get_db_field($direction)) return $args;
        $args[$direction] = $args['items'];
        return $args;
    }

    /** Meta Box 1.14.0 supports a single clause or one flat AND/OR group. */
    public static function restore($args) {
        if (!class_exists('MB_Relationships_API') || !is_array($args)) return $args;
        if (!isset($args['relation'])) return self::restore_clause($args);
        if (!in_array($args['relation'], ['AND', 'OR'], true)) return $args;
        foreach ($args as $key => $clause) {
            if ($key !== 'relation') $args[$key] = self::restore_clause($clause);
        }
        return $args;
    }

    public static function repair_query(WP_Query $query) {
        if (!class_exists('MB_Relationships_API')) return;
        // WPGB removes wp_grid_builder after filtering but retains wpgb_inject
        // when copying the query to calculate facet choices and counts.
        $grid = $query->get('wp_grid_builder') ?: $query->get('wpgb_inject');
        if (!is_scalar($grid) || empty($grid)) return;
        $args = $query->get('relationship');
        $restored = self::restore($args);
        if ($restored !== $args) $query->set('relationship', $restored);
    }
}

// MB Relationships 1.14.0 parses post queries at priority 20.
add_action('parse_query', [MB_WPGB_Relationship_Compat::class, 'repair_query'], 19);

Thank you for the information. The setting within the network section was the key.