Use new search bar template on other pages

[RayBB]

After #9146 is merged

Followup from: https://github.com/internetarchive/openlibrary/issues/9086#issuecomment-2093369982

the Author page (https://openlibrary.org/authors/OL107911A/George_Bernard_Shaw)
the My Books Reading Log page (https://openlibrary.org/people/mekBot/books/want-to-read)
the Subject page (e.g. https://openlibrary.org/subjects/biology)

Describe the problem that you'd like solved

Proposal & Constraints

Additional context

Stakeholders

[schu96]

Hi @RayBB I'd like to take on this issue, it looks like the subject page is the only one that needs updating from the list

[RayBB]

@schu96 seems you're right. I've assigned you. Good luck!