Simplify and improve client-side API docs

[Valve]

1. Move complex params into integrations.md docs file
2. Get rid of ambiguous references (BotDetector vs BotDetectorInterface)
3. Simplify the language, make client-side docs from the point of view of a pure client-side JS developer, not from a pov of a fullstack developer
4. Every entity should have a deeplink in the API docs and be referenced from all places
5. Doc sections, common to both client and server APIs (response, error handling etc) should be in their own file, referenced from both api doc files.
6. Simplify everything overall as much as possible.