Remove /api/v1/chat and the chat agent once the backend chat module is gone

[daniilperkin]

Parent Story

Part of SprintStartProject/Wiki#319. Follow-up cleanup: /api/v1/chat is only called by the backend chat module, which sprintstart-backend#260 removes.

Blocked by sprintstart-backend#260 (backend chat-module removal). The other prerequisite landed 2026-10-02: sprintstart-ai#206 mounted GrepTool and the reasoning streaming in Buddy's search-only mode, so those must not be deleted with the chat agent.

Scope

• Remove api/routes/chat.py and its router registration (api/app.py), the orchestrator factory in api/dependencies.py (OrchestratorFactory, ChatOrchestrator import), the ChatAgent / ChatOrchestrator exports in agents/__init__.py, agents/chat_agent.py (ChatAgent), agents/orchestrator.py (ChatOrchestrator) and the chat-only schemas (ChatRequest, legacy prompt/context field mapping)
• Keep: agents/tools/grep.py (the Buddy turn mounts GrepTool after ai#206), agents/tools/retrieve.py and tools/base.py if anything outside the chat agent still references them, the filter schema reused by BuddyAgentRequest, api/routes/title.py (/api/v1/generate-title, used for Buddy titles)
• Update AGENTS.md: its architecture section describes ChatAgent as the chat engine, "Conventions" says "Chat is one agent, one loop" (restate it for the Buddy turn), and "Project separation" lists ChatRequest
• sprintstart chat CLI: scripts/sprintstart.py registers a chat subcommand (scripts/chat_cli.py) that streams from /api/v1/chat. Remove it, or point it at the Buddy route with capabilities off
• AGENT.md and README.md also describe the chat agent: update them with AGENTS.md
• Remove the tests for deleted code

Acceptance Criteria

• /api/v1/chat is gone; Buddy routes and title generation still work
• No script or CLI calls /api/v1/chat
• No dead imports of chat_agent / orchestrator
• AGENTS.md describes the Buddy agent as the one conversation engine
• Gates pass: uv run ruff format --check ., uv run ruff check ., uv run pyright src/, uv run pytest