fix(cache-warming): accurate cache rate + expectedCacheRate (retention) metric

The Claude cache % read 100% whenever anything was cached, because the metric's
denominator (inputTokens) excluded cached tokens on Anthropic. Fixed upstream in
../claude/provider-anthropic (inputTokens = total prompt); this commit adds the
companion retention metric and exposes it:
- transport-contract: WarmResponse += expectedCacheRate
- transport-http: POST /chat/warm returns expectedCacheRate = cacheRead/(cacheRead+cacheWrite)
- cache-warming: computeExpectedCacheRate + a per-conversation 'cache retention' surface stat
- handoff: documents the fix + cache-rate vs expected-cache (cross-turn) for the FE

Live-verified vs claude haiku: real turn cache rate 61% (was inflated 100%);
warm within TTL expectedCacheRate=100%, after expiry=0%.

1 files changed, 2 insertions, 0 deletions

diff --git a/packages/transport-http/src/app.ts b/packages/transport-http/src/app.ts
index a8cef51..84c7d20 100644
--- a/packages/transport-http/src/app.ts
+++ b/packages/transport-http/src/app.ts
@@ -10,6 +10,7 @@ import { Hono } from "hono";
 import { cors } from "hono/cors";
 import {
 	computeCachePct,
+	computeExpectedCacheRate,
 	isParseError,
 	isSinceSeqError,
 	parseChatBody,
@@ -284,6 +285,7 @@ export function createApp(opts: CreateServerOptions): Hono {
 			cacheReadTokens: result.cacheReadTokens,
 			cacheWriteTokens: result.cacheWriteTokens,
 			cachePct: computeCachePct(result.inputTokens, result.cacheReadTokens),
+			expectedCacheRate: computeExpectedCacheRate(result.cacheReadTokens, result.cacheWriteTokens),
 		};
 		return c.json(response, 200);
 	});