Add a global search bar to docs for faster feature and API discovery

[mfaeezshabbir]

Is your feature request related to a problem? Please describe.
Finding specific features or API references in the docs is slower than it needs to be. I end up scrolling through sections trying to remember where everything lives. It breaks momentum when I’m building.

Describe the solution you'd like
A proper search bar in the docs that gives instant results and helps users jump straight to any feature, API, or guide. Real time filtering would make the whole docs experience feel more premium and more aligned with modern dev tooling.

Describe alternatives you've considered
Scrolling manually. Searching the repo. Both feel outdated and don’t match the velocity Dockview is built for.

Additional context
I’d like to work on implementing this feature as well. I’m happy to take point on the design and development so we can get a smooth developer experience baked right into the docs.