Search: Filter content on the site to auto link and open search overlay.

### Impacted plugin

Jetpack

### What

Entity detection and auto linking to improve on site engagement.

### How

There could be a few different ways to implement this, but we could make Search more useful by auto-linking content (just add a WP filter on the content) to open the search UI and filter by particular keywords.

Some quotes from a DM conversation I had with @georgestephanis that I've been trying to figure out how we could meet some of these desires with the current set of products we have. A tie in to Search feels like the best way.

> Was wondering about feasibility of suggesting new tags for sites based on content — either on a single post in-gutenberg “It looks like you’re writing about x, y, z — click to add these as tags to this post” — or a bulk catch-up page of “It looks like your blog talks a lot about these new topics — x, y, z — and with one click create them as a tag and automatically add some suggested posts to that tag. Possibly also a way of finding existing posts that the admin forgot to tag at the time but with es we can suggest they add them after the fact as an audit?

> the idea is they want to set up “noun pages” to sort of auto-tag stuff and make it easier to find cross-post content on a given topic and maybe do hovercards recommending it kinda like crunchbase does for companies and the like

Some of this overlaps with auto-extracting "answers" (https://github.com/Automattic/jetpack/issues/9174) from content. I feel like we've also had more than a few requests that we currently solve by having people implement [the hacky add-this-magic-stuff-to-your-link-to-open-the-overlay](https://jetpack.com/support/search/install-search-on-your-site/#customize-filters). I wonder if we could have a solution that makes it easier to both manually and automagically add links that trigger immediate filtering and discovery.

Crunchbase currently seems to implement this with custom taxonomies for things like "organizations", "people", etc. and then detects and links to the pages for those entities. Entity detection is probably something we could do, but even just auto populating a custom taxonomy and then using that to populate and trigger opening the overlay. This also overlaps with https://github.com/Automattic/jetpack/issues/17704. https://taxopress.com/ seems to have some of this functionality also.

No implementation files or tests are identified. Start by reviewing Jetpack Search's customization guidance for opening and filtering the overlay, then read related issues 9174 and 17704 to understand overlap. The work is not ready until the entity-detection, taxonomy, linking, and overlay behavior have an agreed scope.

Written by the indexing model from the issue text.