Plan D: web Socket.IO bridge + LangGraph retirement - #8

Plan D — Web bridge + LangGraph retirement

Makes the parallel engine the sole orchestrator and gives it a live web UI. Stacked on #7 (Plan C) — merge #7 first, then this (GitHub retargets to main once #7 lands).

What this does

• backend/main.py now drives the engine over Socket.IO. start_project boots a real engine run (state server + worker subprocesses, human-approval mode); a snapshot-diff poller translates engine state into the React frontend's existing events (agent_status, phase_complete, approval_required prd/plan, budget_update). approve/reject → submit_approval. So the existing React graph UI renders live engine runs — the old working web UI is preserved, now engine-backed.
• run.start_run()/stop_run() — a reusable, self-cleaning run handle extracted from run_pipeline (atomic: tears down on mid-spawn failure).
• backend/engine/webbridge.py — pure, unit-tested snapshot→frontend mappers (incl. the discrete budget-threshold bucket {0,50,75,85,95,100} the frontend meter expects, and a "downgraded" agent status when budget swaps a model).
• LangGraph retired. backend/graph.py + backend/orchestrator.py + ~13 coupled/obsolete tests deleted; langgraph + langgraph-checkpoint-sqlite deps and the mypy override dropped. Zero legacy references remain.

Evidence

• Every task went through TDD + independent spec/quality review (Tasks 1 & 2 each took a Critical fix; Task 3's run-leak findings were fixed — completed runs now stop_run + a FastAPI lifespan shutdown() reclaims everything). Final opus whole-branch review: ready-to-merge (one Important frontend-id mismatch, qa→qa_test, fixed here and confirmed with tsc --noEmit).
• CI-green: ruff 0, black clean, pytest tests/ = 154 passed, 86.93% coverage (gate 70%). Frontend type-checks.

Manual check + tracked follow-ups (not blocking)

• Live browser render is the one manual check (run python -m backend.main + cd frontend && npm run dev) — the emitted event shapes are reproduced verbatim from frontend/src/types/index.ts and every phase-worker node id now matches the engine.
• Bounded lifecycle gaps for a single-user tool (no start_project dedup / disconnect teardown / poller-retry — all reclaimed at server shutdown), the design-inherited in-memory-only load_project after restart, and the ADR-only (vs combined) plan-gate card are noted as follow-ups.