Add Site Search

[brianhawthorne]

Please describe the new feature.

Similar to the site search afforded by pydata-sphinx-theme doc site:

Favor PageFind for implementation: https://pagefind.app/

Integration Tips:

• https://www.unravelled.dev/integrating-pagefind-hugo-and-azure-static-web-apps/
• https://blog.jverkamp.com/2023/09/25/adding-local-search-to-hugo-with-pagefind/
• https://discourse.gohugo.io/t/hugo-pagefind-questions/45222

Add any other context about the new feature here, screenshots, etc.

No response

[brianhawthorne]

PR: https://github.com/scientific-python/scientific-python-hugo-theme/pull/615/files