[Docs]: One conversation engine after the chat → Buddy migration

[daniilperkin]

Parent Story

Part of #319 (chat → Buddy migration). Last step: after the code is gone, the docs must stop describing two conversation engines.

Blocked by SprintStartProject/sprintstart-frontend#206 (chat surface removed). Best done after SprintStartProject/sprintstart-backend#260 and SprintStartProject/sprintstart-ai#207, so the docs describe the final state.

Docs that describe chat today (checked 2026-09-25)

Repo	Files
Wiki	docs/source/tutorials/getting-started/getting-started-ai.md, docs/source/references/definition-of-done.md (the usability-test pages mention chat too, but they are historical records: leave them)
sprintstart-frontend	AGENTS.md (features/chatbot, ChatProvider in the structure list), README.md, docs/FRONTEND_ARCHITECTURE.md
sprintstart-ai	AGENTS.md and AGENT.md (ChatAgent as the chat engine), README.md
workspace root (not in Git)	ARCHITECTURE.md (documents the chat module, chatbot and chat SSE), GEMINI.md

No committed backend doc mentions chat on dev. A local, untracked docs/modulith_boundaries.md lists the chat module: update it if it gets committed.

ADR: add docs/source/explanations/adrs/adr-017-retire-chat-buddy-single-conversation-surface.md (the next free number; the latest is ADR-016) and list it in the ADR index. It records Wiki#319's decisions: one engine, a project per conversation, the backfill keeping chat ids, conversations replacing visits, admin access dropped, batch reasoning, and what was not ported.

Changes

• One conversation engine: Buddy. Capabilities on means a mentor with tools; capabilities off means a grounded search with search_docs + grep and citations.
• Named conversations with an optional project; FAQ and Knowledge Gaps are fed from project-scoped conversations.
• Remove or redirect every mention of /chat, ChatAgent, features/chatbot and the chat module.
• Record the decisions from Wiki#319 (visits replaced by conversations, admin chat access dropped, what was not ported) in a Wiki architecture page or an ADR.

Acceptance Criteria

• No doc describes /chat, ChatAgent or the chat module as current
• The Wiki describes Buddy as the one conversation engine
• ADR-017 is written and listed in the ADR index
• The Wiki builds (make html)