feat: Phase 4-5 — demo mode, polish, deploy, and bug fixes

Add demo mode with mock data provider, Docker deployment, Playwright
tests, PostHog analytics, error boundaries, and SEO metadata. Fix
residences API response unwrapping, kanban drag-and-drop with optimistic
updates, trailing slash proxy redirects, and column name mismatches with
Go API.

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

src/components/layout/top-bar.tsx

@@ -11,9 +11,11 @@ import {
   DropdownMenuSeparator,
   DropdownMenuTrigger,
 } from '@/components/ui/dropdown-menu';
+import { useDataProvider } from '@/lib/demo/data-provider-context';
 
 export function TopBar() {
   const router = useRouter();
+  const { basePath } = useDataProvider();
 
   const handleLogout = async () => {
     try {
@@ -21,7 +23,11 @@ export function TopBar() {
     } catch {
       // Continue with redirect even if the API call fails
     }
-    router.push('/login');
+    if (basePath.startsWith('/demo')) {
+      router.push('/demo');
+    } else {
+      router.push('/login');
+    }
   };
 
   return (
@@ -39,18 +45,18 @@ export function TopBar() {
       <NotificationBell />
       <DropdownMenu>
         <DropdownMenuTrigger asChild>
-          <button className="flex items-center gap-2 rounded-full outline-none focus-visible:ring-2 focus-visible:ring-ring focus-visible:ring-offset-2">
+          <button aria-label="User menu" className="flex items-center gap-2 rounded-full outline-none focus-visible:ring-2 focus-visible:ring-ring focus-visible:ring-offset-2">
             <Avatar>
               <AvatarFallback>U</AvatarFallback>
             </Avatar>
           </button>
         </DropdownMenuTrigger>
         <DropdownMenuContent align="end" className="w-48">
-          <DropdownMenuItem onClick={() => router.push('/app/settings')}>
+          <DropdownMenuItem onClick={() => router.push(`${basePath}/settings`)}>
             <User className="size-4" />
             Profile
           </DropdownMenuItem>
-          <DropdownMenuItem onClick={() => router.push('/app/settings')}>
+          <DropdownMenuItem onClick={() => router.push(`${basePath}/settings`)}>
             <Settings className="size-4" />
             Settings
           </DropdownMenuItem>