Feature: add kapa.ai service to the site

https://www.kapa.ai/ is a good service for working with unstructure data.

It could be great to use it for work with our documentation on site.

Clickhouse already uses it. Here how it happens - https://www.kapa.ai/blog/driving-users-to-mcp

Start by reviewing the site documentation and the Kapa.ai example linked in the issue, including ClickHouse's described use case. No repository file, test, or entry point is named, so first clarify the intended integration, scope, and acceptance criteria; done should mean the agreed Kapa.ai documentation experience is implemented and verified on the site.

Written by the indexing model from the issue text.