With the lunr-extension: https://gitlab.com/antora/antora-lunr-extension, we can trivially add documentation search to individual library pages. This currently does not work with boostlook. I can change my UI bundle to the default Antora one which gives me the search bar but also comes with the other baggage in the top bar:
The gitlab page for the antora-lunr-extension has instructions on how to make your custom UI work with it.