WordPress' default search is lacking. I had "improved" our search with a simple plugin called Relevanssi Light. However, it was still not to my liking. I noticed that Relevanssi Light has a boolean search mode (enabled through code snippet). I enabled it. Now our on-site search is "decent" with good queries. (Links to information about the plugin/code snippet in my post if you want to try it on your WordPress site).

https://thenewleafjournal.com/implementing-boolean-search-on-nlj/