The runtime cutover to Kagi's V1 search API landed in #1272 but
docs/tools/web_search.md still described the sunset V0 endpoint
(GET /api/v0/search with 'Authorization: Bot ...'). Realigned the
Querying and Output bullets with the actual implementation in
packages/coding-agent/src/web/kagi.ts:
- POST https://kagi.com/api/v1/search with Bearer auth and JSON body.
- recency maps to filters.after as a UTC YYYY-MM-DD string.
- Output now includes the categorized bucket merge (search/video/news/
infobox with title tags), adjacent_question + related_search related
questions, direct_answer-derived answer, and meta.trace requestId.
Fixes#2009