Apply custom styles on the Search page

**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.