Closes #30267

This ensures they do not differ in color as described in the issue.

Currently: 
<img width="1182" alt="grafik"
src="https://github.com/user-attachments/assets/7ccc5116-f6b4-4ffc-80fc-b5b51c49a8f2"
/>

This PR: 
<img width="1182" alt="grafik"
src="https://github.com/user-attachments/assets/dcff631a-c1a8-423e-847c-8678a77e7a8e"
/>

Alternatively, we could potentially color the surrounding containers
with the editor background, but I think this way around is more
reasonable for the toolbar.

Release Notes:

- Improved background coloring for search inputs located in the toolbar.