fix(ui): chat background covers full screen regardless of glassmorphism

Previously the background was applied directly to <Page> (room view
only) when glassmorphism was off, and to document.body only when
glassmorphism was on. This caused two bugs:
- Without glassmorphism: background only visible in the chat panel,
  not behind the sidebar
- With glassmorphism: Page reverted to its opaque theme surface color,
  so the body background only showed through the glass sidebar

Fix: SidebarNav now always applies the active background to
document.body (regardless of glassmorphism). RoomView's <Page> is
made transparent whenever a background is active so the body
background shows through both the sidebar and the chat area.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/app/pages/client/SidebarNav.tsx

@@ -40,7 +40,9 @@ export function SidebarNav() {
   // Fix: mirror the active chat background onto document.body so the sidebar blurs through it.
   useEffect(() => {
     const { style } = document.body;
-    if (!glassmorphismSidebar) {
+    const hasBg = chatBackground !== 'none' || glassmorphismSidebar || lotusTerminal;
+
+    if (!hasBg) {
       style.removeProperty('background-image');
       style.removeProperty('background-color');
       style.removeProperty('background-size');
@@ -48,13 +50,15 @@ export function SidebarNav() {
       style.removeProperty('animation');
       return;
     }
-    const effectiveBg = chatBackground === 'none' ? 'tactical' : chatBackground;
+
+    const effectiveBg = chatBackground !== 'none' ? chatBackground : 'tactical';
     const bgStyle = getChatBg(effectiveBg, isDark, pauseAnimations);
     style.backgroundImage = (bgStyle.backgroundImage as string | undefined) ?? '';
     style.backgroundColor = (bgStyle.backgroundColor as string | undefined) ?? '';
     style.backgroundSize = (bgStyle.backgroundSize as string | undefined) ?? '';
     style.backgroundPosition = (bgStyle.backgroundPosition as string | undefined) ?? '';
     style.animation = (bgStyle.animation as string | undefined) ?? '';
+
     return () => {
       style.removeProperty('background-image');
       style.removeProperty('background-color');