feat: persistent context-window tracker in ChatPane

Adds a floating popover above the chat input showing current
context-window usage. Modeled on Paseo's tracker.

- New hook useChatContextStats(chatId, messages) finds the latest
  assistant message in the chat with both ctx_used and ctx_max set,
  computes percent, and returns null when data unavailable.
- New component ChatContextPopover renders a small card with the
  "Context window" label, big percent, and "used / max tokens"
  subline. Hidden when stats is null.
- Color thresholds: <60% muted, 60-85 amber, >85 destructive.
- Not a portal — absolutely positioned inside a new relative
  wrapper around ChatInput in ChatPane.tsx, so it's pane-local
  (multi-pane safe).
- Live updates via the existing messages-array dependency.
- No API / schema / WS changes.

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

apps/web/src/hooks/useChatContextStats.ts

@@ -0,0 +1,37 @@
+import { useMemo } from 'react';
+import type { Message } from '@/api/types';
+
+export interface ChatContextStats {
+  used: number;
+  max: number;
+  percent: number;
+}
+
+/**
+ * Returns the latest context-window usage for the given chat, derived from the
+ * assistant message (with both ctx_used and ctx_max populated) having the most
+ * recent created_at. Returns null when no such message exists.
+ *
+ * Re-evaluates whenever the `messages` reference or `chatId` changes, which
+ * matches the cadence of streaming updates from `useSessionStream`.
+ */
+export function useChatContextStats(
+  chatId: string,
+  messages: Message[],
+): ChatContextStats | null {
+  return useMemo(() => {
+    let latest: Message | null = null;
+    for (const m of messages) {
+      if (m.chat_id !== chatId) continue;
+      if (m.role !== 'assistant') continue;
+      if (m.ctx_used == null || m.ctx_max == null) continue;
+      if (!latest || m.created_at > latest.created_at) latest = m;
+    }
+    if (!latest || latest.ctx_used == null || latest.ctx_max == null) return null;
+    const used = latest.ctx_used;
+    const max = latest.ctx_max;
+    if (max <= 0) return null;
+    const percent = Math.round((used / max) * 100);
+    return { used, max, percent };
+  }, [chatId, messages]);
+}