feat(16-04): install TanStack Router and add shadcn/ui base components

Add @tanstack/react-router, @tanstack/router-plugin (Vite plugin for
file-based route generation), and Radix UI primitives. Configure
TanStackRouterVite plugin before React plugin in vite config. Add four
foundational shadcn/ui components: button, badge, card, dropdown-menu.

packages/web/package.json

@@ -12,6 +12,7 @@
   "dependencies": {
     "@codewalk-district/shared": "*",
     "@tanstack/react-query": "^5.75.0",
+    "@tanstack/react-router": "^1.158.0",
     "@trpc/client": "^11.9.0",
     "@trpc/react-query": "^11.9.0",
     "class-variance-authority": "^0.7.1",
@@ -22,7 +23,10 @@
     "tailwind-merge": "^3.4.0"
   },
   "devDependencies": {
+    "@radix-ui/react-dropdown-menu": "^2.1.16",
+    "@radix-ui/react-slot": "^1.2.4",
     "@tailwindcss/typography": "^0.5.19",
+    "@tanstack/router-plugin": "^1.158.0",
     "@types/node": "^25.2.0",
     "@types/react": "^19.0.0",
     "@types/react-dom": "^19.0.0",