Should I reset $wp_query?

The query is right and its working. But should I reset something?

Yes!

Should I reset them both or just one of them, or is it fine like above?

Neither!

Your WP_Query object is self contained in $query, so there’s no reason to touch the $wp_query global variable, why would you? $wp_query represents the main query, so leave it alone.

What you need to reset, is the current post. Notice $query->the_post() sets the current post, you need to undo that after the loop ends:

    if( $query->have_posts() ) {
        while( $query->have_posts() ) {
            $query->the_post();
            ....
        }
        wp_reset_postdata();
    }

A Word on wp_reset_query()

The wp_reset_query() function is something you might see in your research, but avoid this. It’s intended to clean up after query_posts, which is a function you should never use.

If you ever find yourself needing to use query_posts, or wp_reset_query in your client work, something has gone terribly wrong. Scrub these from your memory, scream when you see them in code, and refactor them with extreme predjudice.

Shortcodes and Blocks

Have you considered turning this into a GB block instead of a shortcode? Just create a block that’s rendered in PHP, there’s no need to learn React or advanced JS