`SearchField` has white background on `form`, not the input field

[adamstankiewicz]

Playground Example

Note the white background on the form in the SearchField component between the input field and the "Search" button CTA.

### Tasks
- [ ] Ensure the `SearchField` input field has a white background, but no white background should appear in the gap between the input field and the "Search" CTA button.

[monteri]

https://github.com/openedx/paragon/pull/2671