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.

2 files changed, 41 insertions, 15 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")
diff --git a/packages/core/src/types/index.ts b/packages/core/src/types/index.ts
index abade27..a1fd2a8 100644
--- a/packages/core/src/types/index.ts
+++ b/packages/core/src/types/index.ts
@@ -143,6 +143,29 @@ export interface UsageData {
 	cacheWriteTokens: number;
 }
 
+/**
+ * Aggregate per-tab usage telemetry: the cumulative sum across ALL persisted
+ * `usage` rows, the request count, and the most recent request's split. This is
+ * the server-side source of truth (complete regardless of frontend
+ * eviction/pagination) returned by `getUsageStatsForTab`. Structurally
+ * identical to the frontend `CacheStats` so it can seed it directly. `null` when
+ * the tab has no usage rows.
+ */
+export interface UsageStats {
+	inputTokens: number;
+	outputTokens: number;
+	cacheReadTokens: number;
+	cacheWriteTokens: number;
+	/** Number of LLM requests (usage rows) counted. */
+	requests: number;
+	last: {
+		inputTokens: number;
+		outputTokens: number;
+		cacheReadTokens: number;
+		cacheWriteTokens: number;
+	} | null;
+}
+
 export type ChunkData =
 	| TextData
 	| ThinkingData
@@ -249,8 +272,16 @@ export type AgentEvent =
 	 * fold its transient live representation into the sealed chunk log. Emitted
 	 * after `status: idle`/`error` (which fire before the DB write). Display/sync
 	 * only — not conversation content.
+	 *
+	 * Carries `usageStats`: the tab's authoritative usage aggregate read from the
+	 * DB AFTER the turn's usage rows were written. The frontend REPLACES (not adds)
+	 * its live `cacheStats` with this, reconciling the live accumulator to the
+	 * persisted truth every turn. This self-heals the live overshoot that occurs
+	 * when a rate-limited fallback attempt's usage is streamed live but then
+	 * discarded server-side (never persisted). `null` ⇒ tab has no usage rows;
+	 * absent ⇒ leave `cacheStats` untouched (back-compat).
 	 */
-	| { type: "turn-sealed"; turnId: string }
+	| { type: "turn-sealed"; turnId: string; usageStats?: UsageStats | null }
 	| { type: "text-delta"; delta: string }
 	| { type: "reasoning-delta"; delta: string }
 	/**