Search Widget: default to non-expanded filter form

#### Steps to reproduce the issue

1. Start from a site with Jetpack Professional, and with the Search feature enabled.
2. Go to Appearance > Customize, and add the Jetpack Search widget to your site.
3. Removing the only filter option and then saving, brings it back again.


4. Ideally, maybe we should default to the "Add Filter" button at all times.

No file or test is named. Reproduce the behavior in Appearance > Customize with the Jetpack Search widget, then locate the widget implementation and its save behavior. Done means removing the only filter remains removed and the widget defaults to showing the “Add Filter” button rather than an expanded filter form.

Written by the indexing model from the issue text.