[task] adopt new orama search components from the website

[ovflowd]

As we migrated to the new Orama components on Node.js's Website that are compatible with SSR, we should adopt them here. This is both for performance and UX.

[ovflowd]

cc @nodejs/web-infra wonder who's interested on this :)

[ovflowd]

This is the upstream PR on nodejs.org (apps/site) nodejs/nodejs.org#8175