For replace <h3> tag with <span> you need to override and modify the module's template
It is located here - modules\mod_articles_good_search\tmpl\Default\
E.g. for fix it for tag field, modify this file - mod_articles_good_search\tmpl\Default\fields\basic\tag.php
And for custom fields - mod_articles_good_search\tmpl\Default\fields\custom_fields\select.php
I try to respect the Hx hierarchy because I have already seen terms well indexed by search engines when they do not add anything.
I will probably always put your module below the title H1 to facilitate the choice of the member.
Any hx tag will break the hierarchy, I will prefer a span or you leave the choice in a module parameter.
Here is an article from a good French SEO in whom I trust
thank you for your attention