fix: align compaction cuts and native usage accounting

app/api/activity/route.ts

@@ -1,8 +1,8 @@
 /**
  * GET /api/activity — the dock's one poll: every running background
  * process, every view (chat, home, everywhere). Composition only — the
- * feed lives in server/observability.ts; cost folds client-side via
- * core/prices.ts. See that module's header for why /api/jobs stays
+ * feed lives in server/observability.ts; costs are projected server-side
+ * through Pi's catalog and public calculator. See that module's header for why /api/jobs stays
  * chat-scoped and untouched.
  */
 import { activityFeed } from "@/src/server";

app/api/chats/[id]/route.ts

@@ -1,4 +1,4 @@
-import { compactionInFlight, deleteChatSession, getChat, isTurnRunning, sessionCoverage, stores, type ChatDeleteMode } from "@/src/server";
+import { compactionInFlight, deleteChatSession, getChat, isTurnRunning, sessionCoverage, sessionCost, stores, type ChatDeleteMode } from "@/src/server";
 
 export async function GET(_req: Request, { params }: { params: Promise<{ id: string }> }) {
 	const { id } = await params;
@@ -17,6 +17,7 @@ export async function GET(_req: Request, { params }: { params: Promise<{ id: str
 	return Response.json({
 		...chat,
 		messages: chat.messages,
+		pricing: sessionCost(chat),
 		turnInFlight: isTurnRunning(id),
 		compacting: compactionInFlight(id),
 		coverage: sessionCoverage(id),

app/api/graph/costs/route.ts

@@ -4,7 +4,7 @@
  * three usage channels (chat extraction runs, notes-source runs,
  * cluster-naming runs). Thin transport over src/server's graphCosts();
  * the fold itself is pure core (core/cost-summary.ts). Dollars are
- * inferred from PRICES at read time — never stored, so a price sync
+ * inferred from Pi's catalog/calculator at read time — never stored, so a catalog update
  * re-prices the whole history for free.
  *
  * Scope (user-decided): the graph pipeline ONLY — teaching turns and