Search: display results natively in the theme without an overlay

> I’m very disappointed with this change. I want my search to feel like a native experience. Why an overlay UI? If you have to add that in, can you please add an option to deactivate the overlay UI? I know you are trying to improve UX but this is just not in the right direction for many of us. I run a store and I want to only search for products. Search results need to share a common display with categories. Please, oh please, tell me this is still possible!

https://jetpack.com/2020/04/07/the-new-jetpack-search-architecture/#comment-197526

We [experimented with this in the prototype](https://jetpack.com/2019/11/05/79-peek-future-jetpack-search/) and did somewhat have it working, but it did not integrate well with a lot of themes. We could potentially bring this back as an option.

Start with the Jetpack Search architecture and prototype links in the issue; no repository files, tests, or entry points are identified. Clarify whether the goal is an optional native theme results view or removal of the overlay, then define completion as search results sharing the theme's display with categories.

Written by the indexing model from the issue text.