Generally speaking, "hyphen" is prefered over "underscore" - I never had anyone use "periods" before, but for the sake of this question, I recommend hyphens over periods. It is more a readability thing. However, it will neither make or break your site. The only thing that matters when it comes to SEO is that you have a product/service that is needed by people, content that supports search queries of different intent (knowledge, commercial, transactional) and resonates with your audience.
Equally important - have an outreach campaign in place that works. Finally, a desktop and mobile-friendly website that passes the UI/UX needs of your visitors (see RAIL model). That's all based on eight years working in Digital Marketing and various successful projects. The website is your car, and Technical SEO, content and outreach is the driver. The vehicle must be optimised and ready - the driver will win the race.
Now to answer your particular question - you are referring to a Search query - so I am assuming this is a POST request (you are sending the "Search" Query entered by a user to the Server). So it doesn't matter at all to SEO because Google bot will not invoke a search on your website, most importantly it won't enter a random long-tail keyword and then check the POST URL and try to make sense of it (ironically of the search term it just entered).
Google bot will only ever crawl links in your sitemap and links found on your website .
Please let me know if I miss understood your question, and I am more than happy to give additional information.