feat(09-05): ThemeSessionBridge + ThemeToggle write-through to /api/me/theme

- Create ThemeSessionBridge.tsx: useEffect compares session.user.theme to
  next-themes value; calls setTheme(serverTheme) on mismatch; validates
  against 3-string allowlist ('light'|'dark'|'system'); renders null
- Mount <ThemeSessionBridge /> as first child of <AuthProvider> in app/layout.tsx
- Modify ThemeToggle: writeTheme() calls setTheme() then fire-and-forget
  PUT /api/me/theme; silent catch for network errors (best-effort desktop UX)

components/mobile/profile/ThemeSessionBridge.tsx

@@ -0,0 +1,38 @@
+'use client';
+
+/**
+ * ThemeSessionBridge (THEME-03 / D-16, D-17).
+ *
+ * On session load and after sign-in, compares session.user.theme to the
+ * next-themes useTheme() value and calls setTheme(session.user.theme) if
+ * different. Server is canonical; this is the bridge that enforces it.
+ *
+ * Renders nothing.
+ */
+
+import { useEffect } from 'react';
+import { useTheme } from 'next-themes';
+import { useSession } from '@/lib/auth-client';
+
+type SessionUserWithTheme = { theme?: 'light' | 'dark' | 'system' | string };
+
+export function ThemeSessionBridge() {
+  const { data: session } = useSession();
+  const { theme, setTheme } = useTheme();
+
+  useEffect(() => {
+    if (!session?.user) return;
+    const serverTheme = (session.user as SessionUserWithTheme).theme;
+    if (
+      serverTheme === 'light' ||
+      serverTheme === 'dark' ||
+      serverTheme === 'system'
+    ) {
+      if (serverTheme !== theme) {
+        setTheme(serverTheme);
+      }
+    }
+  }, [session?.user, theme, setTheme]);
+
+  return null;
+}