Studio: Fix SearchControl margin bottom styles to ensure compatibility with the new component version

[ivan-ottinger]

Related issues

• Fixes https://github.com/Automattic/dotcom-forge/issues/9652.

Proposed Changes

• add __nextHasNoMarginBottom={ true } prop that removes margin bottom built into the SearchControl component
• add margin bottom back using the className prop

Testing Instructions

1. Check out the PR and build the app with STUDIO_SITE_SYNC=true npm start.
2. Open browser inspector.
3. Navigate to the Sync tab of a particular site and click on the Connect site button.
4. There should be no Bottom margin styles for wp.components.SearchControl is deprecated since version 6.7 [...] warning displayed in the console (as described in the related issue: https://github.com/Automattic/dotcom-forge/issues/9652).
5. There should still be a margin bottom separating the SearchControl component from the Syncing is supported for sites on the Business plan or above. text below.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

[katinthehatsite]

The changes look good to me and I do not see the warning in the console anymore 👍