feat(ui): paint VK status bar to the app theme (VKWebAppSetViewSettings)

Parity with the Telegram chrome painting: on a VK Mini App launch and on
every theme change, set VK's status-bar appearance (and, on Android, the
action/navigation bar colours) from the app's live theme tokens, so the VK
chrome matches the UI instead of clashing.

syncVKChrome mirrors syncTelegramChrome; the status-bar appearance is
derived from the --bg token's luminance (appearanceForBg, unit-tested).
Wired into the VK onScheme handler (fires on launch + on theme change) and
setTheme. Docs: UI_DESIGN VK integration.

ui/src/lib/app.svelte.ts

@@ -31,7 +31,7 @@ import {
   telegramCloudGet,
   telegramCloudSet,
 } from './telegram';
-import { onVKPath, insideVK, vkInit, vkDisableSwipeBack, vkLaunchParams, vkUserName, vkStartParam, vkOnScheme, vkOnInsets } from './vk';
+import { onVKPath, insideVK, vkInit, vkDisableSwipeBack, vkLaunchParams, vkUserName, vkStartParam, vkOnScheme, vkOnInsets, vkSetViewSettings, appearanceForBg } from './vk';
 import { haptic } from './haptics';
 import { CLOUD_PREFS_KEY, decodeClientPrefs, encodeClientPrefs } from './cloudprefs';
 import { parseStartParam } from './deeplink';
@@ -552,6 +552,19 @@ function syncTelegramChrome(): void {
   );
 }
 
+/**
+ * syncVKChrome paints VK's status bar (and, on Android, the action/navigation bars) from the app's
+ * live theme tokens, so the surrounding VK chrome matches the UI. A no-op outside VK. Parity with
+ * syncTelegramChrome.
+ */
+function syncVKChrome(): void {
+  if (!insideVK() || typeof document === 'undefined') return;
+  const cs = getComputedStyle(document.documentElement);
+  const bg = cs.getPropertyValue('--bg').trim();
+  const bgElev = cs.getPropertyValue('--bg-elev').trim();
+  void vkSetViewSettings(appearanceForBg(bg), bgElev, bg);
+}
+
 /**
  * syncTelegramSafeArea mirrors Telegram's safe-area insets into CSS vars: the content-safe-area top
  * (the height Telegram's native nav overlays the viewport in fullscreen) into --tg-content-top
@@ -694,6 +707,9 @@ export async function bootstrap(): Promise<void> {
     // VK mobile webview's prefers-color-scheme does not track it).
     void vkOnScheme((scheme) => {
       if (app.theme === 'auto') applyTheme(scheme);
+      // Repaint VK's status/nav bars to the resolved theme; this handler also fires on launch, so it
+      // covers the initial paint (auto → the VK scheme just applied, explicit → the theme from boot).
+      syncVKChrome();
     });
     // Clear the device safe area from VK's insets — the VK mobile webview does not surface them via
     // CSS env() (notably the Android home bar). max() keeps whichever of env() / the VK value is real.
@@ -995,6 +1011,7 @@ async function reconcileCloudPrefs(): Promise<void> {
 export function setTheme(theme: ThemePref): void {
   app.theme = theme;
   applyTheme(theme);
+  syncVKChrome();
   persistPrefs();
 }