test: add mvp verification plan

apps/web/package-lock.json

@@ -12,6 +12,7 @@
         "svelte": "^5.42.0"
       },
       "devDependencies": {
+        "@playwright/test": "^1.61.1",
         "@testing-library/jest-dom": "^6.9.1",
         "@testing-library/svelte": "^5.2.9",
         "@tsconfig/svelte": "^5.0.5",
@@ -724,6 +725,22 @@
         "@jridgewell/sourcemap-codec": "^1.4.14"
       }
     },
+    "node_modules/@playwright/test": {
+      "version": "1.61.1",
+      "resolved": "https://registry.npmjs.org/@playwright/test/-/test-1.61.1.tgz",
+      "integrity": "sha512-8nKv6+0RJSL9FE4jYOEGXnPeM/Hg12qZpmqzZjRh3qM0Y7c3z1mrOTfFLids72RDQYVh9WpLEfR5WdpNX4fkig==",
+      "dev": true,
+      "license": "Apache-2.0",
+      "dependencies": {
+        "playwright": "1.61.1"
+      },
+      "bin": {
+        "playwright": "cli.js"
+      },
+      "engines": {
+        "node": ">=18"
+      }
+    },
     "node_modules/@rollup/rollup-android-arm-eabi": {
       "version": "4.62.2",
       "resolved": "https://registry.npmjs.org/@rollup/rollup-android-arm-eabi/-/rollup-android-arm-eabi-4.62.2.tgz",
@@ -2000,6 +2017,53 @@
         "url": "https://github.com/sponsors/jonschlinkert"
       }
     },
+    "node_modules/playwright": {
+      "version": "1.61.1",
+      "resolved": "https://registry.npmjs.org/playwright/-/playwright-1.61.1.tgz",
+      "integrity": "sha512-DWnY5o3YbLWK4GovuAVwpqL+1VwGNdUGrRr++8j8PtQQzvAVZUIMjKQ90fY689sEJZJBbZVw1rXaOKSTitkzPQ==",
+      "dev": true,
+      "license": "Apache-2.0",
+      "dependencies": {
+        "playwright-core": "1.61.1"
+      },
+      "bin": {
+        "playwright": "cli.js"
+      },
+      "engines": {
+        "node": ">=18"
+      },
+      "optionalDependencies": {
+        "fsevents": "2.3.2"
+      }
+    },
+    "node_modules/playwright-core": {
+      "version": "1.61.1",
+      "resolved": "https://registry.npmjs.org/playwright-core/-/playwright-core-1.61.1.tgz",
+      "integrity": "sha512-h7Qlt6m4REp25qvIdvbDtVmD4LqVXfpRxhORv9L0jzETM05p4fuPJ3dKyuSXQxDSbXnmS79HAgi9589lGSpLkg==",
+      "dev": true,
+      "license": "Apache-2.0",
+      "bin": {
+        "playwright-core": "cli.js"
+      },
+      "engines": {
+        "node": ">=18"
+      }
+    },
+    "node_modules/playwright/node_modules/fsevents": {
+      "version": "2.3.2",
+      "resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
+      "integrity": "sha512-xiqMQR4xAeHTuB9uWm+fFRcIOgKBMiOBP+eXiyT7jsgVCq1bkVygt00oASowB7EdtpOHaaPgKt812P9ab+DDKA==",
+      "dev": true,
+      "hasInstallScript": true,
+      "license": "MIT",
+      "optional": true,
+      "os": [
+        "darwin"
+      ],
+      "engines": {
+        "node": "^8.16.0 || ^10.6.0 || >=11.0.0"
+      }
+    },
     "node_modules/postcss": {
       "version": "8.5.19",
       "resolved": "https://registry.npmjs.org/postcss/-/postcss-8.5.19.tgz",