fix: reconcile live cacheStats to DB truth on turn-sealed

Addresses the live-accumulator overshoot a Gemini review surfaced: the
frontend adds every streamed usage event to cacheStats, but a rate-limited
fallback attempt's usage is discarded server-side (never persisted). Live
numbers overshot until a reload re-seeded from the DB aggregate.

Fix: turn-sealed (emitted AFTER the atomic usage-row write) now carries the
authoritative getUsageStatsForTab aggregate. The store REPLACES (not adds)
cacheStats with it every turn — landing the just-sealed turn's usage AND
self-healing any live drift, including the discarded-fallback overshoot. No
extra round-trip (piggybacks turn-sealed); idempotent in the happy path.

- core: add UsageStats type; getUsageStatsForTab returns it; turn-sealed gains
  optional usageStats field.
- api: agent-manager reads getUsageStatsForTab post-flush and attaches it to
  the turn-sealed emit (try/catch: omit on DB error).
- frontend: turn-sealed handler replaces cacheStats (undefined ⇒ untouched
  back-compat; null ⇒ clear).

Tests: frontend reconcile/self-heal/back-compat/null-clear; api turn-sealed
carries aggregate. 509 -> 514 passing; typecheck + biome green.

1 files changed, 9 insertions, 14 deletions

diff --git a/packages/core/src/db/chunks.ts b/packages/core/src/db/chunks.ts
index 509cbbd..e0aadf3 100644
--- a/packages/core/src/db/chunks.ts
+++ b/packages/core/src/db/chunks.ts
@@ -5,7 +5,14 @@ import {
 	groupRowsToMessages,
 	type MessageRow,
 } from "../chunks/transform.js";
-import type { ChunkData, ChunkRow, ChunkRowDraft, TextData, UsageData } from "../types/index.js";
+import type {
+	ChunkData,
+	ChunkRow,
+	ChunkRowDraft,
+	TextData,
+	UsageData,
+	UsageStats,
+} from "../types/index.js";
 import { getDatabase } from "./index.js";
 
 // Re-export the DB-free transforms so existing barrel consumers
@@ -173,19 +180,7 @@ export function getTotalChunkCount(tabId: string): number {
  * Sums in JS after selecting the rows (mirroring `mapRow`) to avoid relying on
  * `json_extract` over the freeform `data_json`.
  */
-export function getUsageStatsForTab(tabId: string): {
-	inputTokens: number;
-	outputTokens: number;
-	cacheReadTokens: number;
-	cacheWriteTokens: number;
-	requests: number;
-	last: {
-		inputTokens: number;
-		outputTokens: number;
-		cacheReadTokens: number;
-		cacheWriteTokens: number;
-	} | null;
-} | null {
+export function getUsageStatsForTab(tabId: string): UsageStats | null {
 	const db = getDatabase();
 	const rows = db
 		.query("SELECT data_json FROM chunks WHERE tab_id = $tabId AND type = 'usage' ORDER BY seq ASC")