The stats bar: context + cost beneath the composer, per-turn detail

One quiet row beneath the composer/question shell (not flush to the
screen bottom; static height, outside the morphing shell):

- LEFT: context window + session cost, clickable → per-turn detail
  popover (context, total, unpriced count, one row per turn with
  model/steps/cost). All folds from core/prices.ts — sessionCost,
  contextWindow, turnCost — no cost math in components.
- RIGHT: model + "Thinking —" — a placeholder slot for the coming
  model/thinking-level CONTROL (later work with its contract changes);
  display-only today, model read from the last turn's usage,
  pretty-printed (Glm 5.3 Flash).
- Data: the record's turns log, seeded on mount, refreshed when the
  local stream settles, kept fresh by the existing record re-syncs.
  No turns yet → "—" everywhere; unpriceable turns never fold into a
  fake $0 (the doctrine).
- formatUsd/formatTokens moved to components/usage-format.ts (shared
  with the activity dock); prettyModel joins them, pure + tested.

components/activity-dock.tsx

@@ -5,6 +5,7 @@ import { ActivityIcon, BotIcon, PenToolIcon, PlayIcon, SearchIcon, SquareIcon, W
 import { cn } from "@/lib/utils";
 import type { CallUsage, JobKind, JobRecord } from "@/src/core";
 import { CONTEXT_LIMITS, jobCost } from "@/src/core";
+import { formatTokens, formatUsd } from "@/components/usage-format";
 
 /**
  * THE ACTIVITY DOCK (wave 4, vision observability): the bottom-right corner
@@ -179,18 +180,6 @@ export function formatElapsed(ms: number): string {
 	return `${Math.floor(m / 60)}h ${String(m % 60).padStart(2, "0")}m`;
 }
 
-/** USD for cent-scale money: >= $1 keeps two decimals, smaller keeps four. */
-export function formatUsd(c: number): string {
-	return c >= 1 ? `$${c.toFixed(2)}` : `$${c.toFixed(4)}`;
-}
-
-/** 38000 → "38k", 1234567 → "1.2M" — trimmed, never "38.0k". */
-export function formatTokens(n: number): string {
-	if (n >= 1e6) return `${+(n / 1e6).toFixed(1)}M`;
-	if (n >= 1e3) return `${+(n / 1e3).toFixed(1)}k`;
-	return String(n);
-}
-
 // ─── The dock ─────────────────────────────────────────────────────────────────
 
 /** Narrow viewports (< sm) collapse the dock to a count badge → drawer. */