Search: Search form trigger change of context without user choice

### Impacted plugin
Jetpack

### Issue
Typing text into the search form auto-triggers the search modal. There's a fundamental problem with changing the user context without their choice, but this also creates a more serious bug: if the user attempts to exit the modal using the keyboard (by clicking 'close'), then focus is passed back to the input form, which then automatically re-opens the modal.

This doesn't happen if the user clicks 'close' with a mouse or if the user leaves the modal using the Esc key; but triggering 'close' from the keyboard creates a loop.


### Other Information
This issue was surfaced to team 51 by an a11y contractor working on a partner site.