v2 web interface: fix delivery races, real URLs, optimistic echo, thinking stream, button-based quiz UI

Root causes of the v1 browser bugs (all fixed + covered by deterministic tests):
- duplicated messages: per-socket snapshot + global broadcast marking raced;
  replaced with a single append-only entry log (exactly-once per socket,
  structurally) — covered by tests/server.test.ts
- delayed/missing echo of own messages: optimistic append with sending/failed
  status, reconciled by text when the real entry arrives
- no thinking shown: thinking deltas streamed live (kind: thinking) and
  persisted in assistant entries so they survive reloads
- ask answers graded as wrong: AnsweredCard no longer applies quiz grading to
  ask answers (no ✓/✗, no verdict)
- broken option selection: native radio/checkbox inputs fighting React state
  replaced with button-based options (single source of truth, one-click select)
- no URLs: History API routing — / home, /s/<file> per session (deep links,
  refresh, back button); session view resumes its file on mount
- lost connection = dead UI: exponential-backoff reconnect with full resync
- stick-to-bottom transcript with jump-to-latest pill

Server: startServer() with injectable runtime factory (scripted model in
tests); createSession returns file for routing; scripted model gained thinking
turns. 51 deterministic tests green.

README.md

@@ -34,7 +34,7 @@ npm run graph                        # ledger stats
 Three layers, LLM only at the top:
 
 1. **Unit** (`tests/question-core.test.ts`, `tests/bridge.test.ts`) — pure logic: grading, exact-set matching, option shuffling/index resolution, answer formatting, pending-question re-arm, the bridge state machine. No pi, no network.
-2. **Scripted integration** (`tests/integration-quiz.test.ts`) — the full pi agent loop with real extensions and real session persistence, but the LLM replaced by a scripted fake model (`src/testing/scripted-model.ts`). Deterministically verifies the quiz dispatch contract: question persisted → tool returns immediately → agent ends turn → answer graded → `[Quiz answer]` user message → agent continues → resume re-arms pending questions.
+2. **Scripted integration** (`tests/integration-quiz.test.ts`, `tests/server.test.ts`) — the full pi agent loop with real extensions and real session persistence, but the LLM replaced by a scripted fake model (`src/testing/scripted-model.ts`). Deterministically verifies the quiz dispatch contract: question persisted → tool returns immediately → agent ends turn → answer graded → `[Quiz answer]` user message → agent continues → resume re-arms pending questions.
 3. **Live smoke** (`scripts/e2e.ts`) — real model over real WebSocket. For verifying actual model *behavior* (does it follow the end-your-turn convention?) — which is a prompt-engineering question, verified by using the app, not by CI.
 
 ## Layout