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>

package.json

@@ -6,7 +6,10 @@
     "dev": "next dev",
     "build": "next build",
     "start": "next start",
-    "lint": "eslint"
+    "lint": "eslint",
+    "analyze": "ANALYZE=true next build",
+    "test:e2e": "playwright test",
+    "test:e2e:ui": "playwright test --ui"
   },
   "dependencies": {
     "@dnd-kit/core": "^6.3.1",
@@ -20,17 +23,21 @@
     "date-fns": "^4.1.0",
     "lucide-react": "^0.576.0",
     "next": "16.1.6",
+    "posthog-js": "^1.357.2",
     "radix-ui": "^1.4.3",
     "react": "19.2.3",
     "react-day-picker": "^9.14.0",
     "react-dom": "19.2.3",
     "react-hook-form": "^7.71.2",
     "recharts": "^3.7.0",
+    "sonner": "^2.0.7",
     "tailwind-merge": "^3.5.0",
     "zod": "^4.3.6",
     "zustand": "^5.0.11"
   },
   "devDependencies": {
+    "@axe-core/playwright": "^4.11.1",
+    "@next/bundle-analyzer": "^16.1.6",
     "@playwright/test": "^1.58.2",
     "@tailwindcss/postcss": "^4",
     "@types/node": "^20",