v1.12.2: live tok/s + ctx display next to status indicator

ChatThroughput renders inline beside StatusDot while streaming or
tool_running. Subscribes to existing usage frames via sessionEvents.
Hides when status drops to idle/error or data is older than 10s.

Addresses the 2026-05-21 spike's UX gap where slow streams looked
identical to dead streams — now there's a live token velocity readout
that immediately distinguishes the two.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/web/src/components/MobileTabSwitcher.tsx

@@ -13,6 +13,7 @@ import { toast } from 'sonner';
 import type { Chat, WorkspacePane } from '@/api/types';
 import { BottomSheet } from '@/components/BottomSheet';
 import { StatusDot } from '@/components/StatusDot';
+import { ChatThroughput } from '@/components/ChatThroughput';
 import {
   DropdownMenu,
   DropdownMenuContent,
@@ -206,6 +207,7 @@ export function MobileTabSwitcher({
         >
           <span className="shrink-0 text-muted-foreground">{paneIcon(active?.kind ?? 'chat')}</span>
           <StatusDot chatId={activeChatId} />
+          <ChatThroughput chatId={activeChatId} />
           <span className="truncate flex-1 text-left">{activeLabel}</span>
           <ChevronDown size={14} className="opacity-60 shrink-0" />
         </button>
@@ -237,6 +239,7 @@ export function MobileTabSwitcher({
               >
                 <span className="shrink-0 text-muted-foreground">{paneIcon(pane.kind)}</span>
                 <StatusDot chatId={cid ?? null} />
+                <ChatThroughput chatId={cid ?? null} />
                 {renamingChatId === cid && cid ? (
                   <input
                     autoFocus