You're running into an issue with MySQL's ONLY_FULL_GROUP_BY mode, which enforces strict grouping rules. The error happens because MySQL requires all selected columns that are not part of an aggregate function (like COUNT(), SUM(), etc.) to be included in the GROUP BY clause.

Why Is This Happening? Your query includes:

ORDER BY wp_postmeta.meta_value ASC;

Since wp_postmeta.meta_value is not included in the GROUP BY clause, MySQL complains that it can't determine a single value for ordering.

How to Fix It? If GROUP BY wp_posts.ID is not strictly necessary, you can remove it. Try modifying your function like this:

    if ( 'anyx-training' === $query['post_type']) {
         $query['meta_key'] = "anyx-training-order";
         $query['orderby'] = "meta_value_num";
         $query['order'] = "ASC";
         $query['suppress_filters'] = false; // Ensures WP_Query doesn't suppress the meta query
    }
    return $query;
}
add_filter( 'query_loop_block_query_vars', 'training_qv_anyx_training', 10, 2 );