fix: Fixes the search bar appearance in production

[Marvelousmicheal]

Fixes the search bar appearance in production and brings the rest of the
search modal in line with the brand design.

The bug: a large X rendered across the middle of the search bar, and text
typed into it was invisible. Search itself worked — results came back
correctly — the input just looked empty.

The cause: the header's button styling was also landing on the search
modal's internals, stretching the clear button across the full width of the
input and covering it.

Also: focus states in the search modal were falling back to the browser
default, which follows the OS accent colour and shows up orange on most
machines. The input, the clear button, and the results now all use the brand
green, in both light and dark. Light mode uses the deeper green so the ring
stays legible against white.

Only visible in a production build — the search UI isn't generated in dev.