For the most part, Google doesn't care about what tags you use in your HTML. (The few exceptions being things like titles, meta tags, and structured data.) You could implement your dialogs with <dialog> tags or with <div> tags and it probably won't change your SEO or how Google sees your site.
No matter how they are implemented, dialogs are not ...
You also need to add noindex meta tag in the template page where your search result is dynamically rendered.
<meta name="robots" content="noindex" />
Usually, a CMS like WordPress uses a template page that dynamically renders the search result in your website. You need to add that no index meta tag in to that template page. ...
You can figure this out by using a site query and setting the time tool back as far as possible.
For example search:
Then set the time range to be Jan 1, 1BC - Today
And then the result of that page will have the original date next to it.