Generate docs/api-reference.md from the live FastAPI route table.

The output is the full docs/api-reference.md content: hand-authored narrative sections (static) followed by an auto-generated Route Inventory table derived from app.routes. The route inventory is the drift-checkable surface -- any route added or removed will change the generator's output and fail CI.

Mirrors the mcp_tools_doc() live-reflection approach: the generator owns the canonical file, CI diffs committed vs generated, and drift fails the build.