I can’t tell you how to use “ACF: Better Search”. This is a plugin by another developer and I do not use it.
What I do know is that you cannot alter the “s” parameter in the WP search to include searching a post based on a taxonomy.
You would need to have a separate field that listed the terms in the taxonomy where the value submitted is the term_id for each term. Then you would need to alter the query done during the search to add a tax_query.
Welcome to the Advanced Custom Fields community forum.
Browse through ideas, snippets of code, questions and answers between fellow ACF users