Apply custom styles on the Search page

[martyanovandrey]

Description:
Custom CSS configured for the documentation pages is not applied on the Search page. This leads to inconsistent branding and layout between docs and search.

Current behavior:

• Custom styles are injected on documentation pages only.
• Search page renders without the project’s custom CSS.

Expected behavior:
The same custom CSS configured in the project is injected on the Search page as well.

Steps to reproduce:

• Configure custom styles in the project.
• Build and serve the docs.
• Open any documentation page — custom styles are applied.
• Open the Search page — custom styles are missing.
• Acceptance criteria:

Custom styles are loaded on the Search page identically to documentation pages.
No regressions for projects without custom styles.