Search: Dashboard toggles fail silently upon nonce expiration

### Impacted plugin

Jetpack

### Steps to Reproduce

1. On a site with a Jetpack Search subscription, navigate to the Search Dashboard (`/wp-admin/admin.php?page=jetpack-search`).
2. Wait a while 🙂 (I waited a few hours.)
3. Try interacting with any of the toggles.

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

Either:

- An error message explaining I'd need to refresh the page. Or...
- Automatically refresh the nonce in the background and handle the toggle flip.

### What actually happened

Clicking the toggle does nothing visibly.

### Other information

_No response_

### Operating System

_No response_

### OS Version

_No response_

### Browser

Chrome/Chromium

### Browser Version(s)

_No response_

Start by reproducing the failure in the Jetpack Search Dashboard at /wp-admin/admin.php?page=jetpack-search after the nonce has expired. Trace the toggle request and its expiration response; done means the user either sees an error explaining that the page must be refreshed or the nonce is renewed and the toggle succeeds.

Written by the indexing model from the issue text.