feat: expose cache efficiency metrics in cozempic diagnose (cache hit rate, server tool costs)

[junaidtitan]

Discovery

Every assistant message in the JSONL contains a usage object with full cache and server tool metrics:

{
  "cache_creation": {
    "ephemeral_1h_input_tokens": 45000,
    "ephemeral_5m_input_tokens": 12000
  },
  "cache_read_input_tokens": 38000,
  "input_tokens": 2100,
  "output_tokens": 450,
  "server_tool_use": {
    "web_search_requests": 3,
    "web_fetch_requests": 5
  }
}

Currently cozempic diagnose only shows total token count and context %. It ignores cache efficiency entirely.

New Metrics for diagnose

Cache Efficiency:
  Cache hit rate:      73.2%   (38K of 52K input tokens from cache)
  Cache creation:      12.0K   (ephemeral 5-min) + 4.5K (ephemeral 1-hour)
  Effective cost:      ~0.31x  (cache reads cost ~0.1x vs full input tokens)

Server Tool Costs:
  Web searches:        47      (billed per search)
  Web fetches:         23      (billed per fetch)

Turn-by-Turn Cache Health:
  Turn 1:  0% cache (cold start)
  Turn 5:  45% cache
  Turn 12: 78% cache
  Turn 20: 82% cache ← stable

Why It Matters

Low cache hit rate = the session prompt is changing significantly each turn, destroying cache efficiency. This is often caused by:

• Dynamic content in system prompt (timestamps, git status that changes)
• CLAUDE.md files that change frequently
• Large tool results with timestamps/UUIDs that vary

A Cozempic treatment that stabilizes cache-busting content could save 60-80% of token costs without reducing context size.

Implementation

Add cache_efficiency(messages) to diagnosis.py:

def cache_efficiency(messages):
    total_cache_read = 0
    total_cache_create = 0
    total_input = 0
    total_server_searches = 0
    total_server_fetches = 0
    
    for _, msg, _ in messages:
        if msg.get("type") != "assistant":
            continue
        usage = msg.get("message", {}).get("usage", {})
        total_cache_read += usage.get("cache_read_input_tokens", 0)
        total_cache_create += (
            usage.get("cache_creation_input_tokens", 0) +
            usage.get("cache_creation", {}).get("ephemeral_1h_input_tokens", 0) +
            usage.get("cache_creation", {}).get("ephemeral_5m_input_tokens", 0)
        )
        total_input += usage.get("input_tokens", 0)
        server = usage.get("server_tool_use", {})
        total_server_searches += server.get("web_search_requests", 0)
        total_server_fetches += server.get("web_fetch_requests", 0)
    ...