feat: implement 33 nice-to-have features + fix 37 code review bugs

5 SDD batches archived:
- Batch 1: UI Polish (10 features, 14 tasks)
- Batch 2: Study System (8 features, 23 tasks)
- Batch 3: Infrastructure (5 features, 22 tasks)
- Batch 4: AI Advanced (5 features, 30 tasks) — RAG with @xenova/transformers
- Batch 5: Core Features (5 features, 19 tasks)

37 bugs fixed from comprehensive code review (11 CRITICAL, 12 HIGH, 14 MEDIUM/LOW):
- SSE streaming now works (event.token check)
- API keys no longer exposed via GET /api/models
- FTS5 injection sanitized
- DB backup/restore with admin auth
- Buddy mode wired (buddy_meta column)
- Exam auto-submit stale closure fixed
- CSS variables aligned with design tokens
- Progress data corruption fixed
- WebSocket protocol auto-detection
- Tests infrastructure completed (vitest + node:test)

server/lib/llm.js

@@ -1,6 +1,9 @@
 const Anthropic = require('@anthropic-ai/sdk');
 const OpenAI = require('openai');
 
+// NOTE: model objects carry api_key in memory — avoid logging full model objects.
+// Use model.name or model.provider only in log statements.
+
 /**
  * Normalize Anthropic + OpenAI-compatible streams into one AsyncIterable.
  * Yields: { token, done, fullText } events.