Search: Instant Search is active at /wp-admin/widgets.php

### Impacted plugin

Jetpack, Search

### Steps to Reproduce

1. Install the Search plugin and buy a Search plan.
2. Visit `/wp-admin/widgets.php`
3. Note that an API request is made to the Jetpack Search endpoint in the background.

### A clear and concise description of what you expected to happen.

Instant Search is for the front end of the site and should not be active on `/wp-admin/widgets.php`.

### What actually happened

Instant Search is making an API request from `/wp-admin/widgets.php`.

### Other information

_No response_

### Operating System

_No response_

### OS Version

_No response_

### Browser

Firefox

### Browser Version(s)

_No response_

Reproduce the issue by installing Jetpack Search with a Search plan and visiting /wp-admin/widgets.php while monitoring requests. Trace where Instant Search is initialized for this admin page; done means the page no longer makes a request to the Jetpack Search endpoint, while front-end Instant Search remains active.

Written by the indexing model from the issue text.