test: add playwright with basic tests for home page

package.json

@@ -10,6 +10,7 @@
     "format": "prettier --config .prettierrc 'app/' --write",
     "audit": "npm audit",
     "typecheck": "tsc --noEmit",
+    "test": "playwright test",
     "prepare": "husky install",
     "migrate": "npx prisma migrate dev",
     "generate": "npx prisma generate",
@@ -20,8 +21,10 @@
     "@emotion/styled": "^11.11.0",
     "@mui/lab": "^5.0.0-alpha.170",
     "@mui/material": "^5.15.6",
+    "@playwright/test": "^1.45.1",
     "@prisma/client": "5.8.1",
     "@vercel/analytics": "^1.1.2",
+    "dotenv": "^16.4.5",
     "nanoid": "^5.0.4",
     "next": "^14.2.3",
     "react": "^18",