feat(web): Playwright E2E test suite for critical paths (#152)

Co-authored-by: Jason Woltje <jason@diversecanvas.com>
Co-committed-by: Jason Woltje <jason@diversecanvas.com>

apps/web/package.json

@@ -8,6 +8,7 @@
     "lint": "eslint src",
     "typecheck": "tsc --noEmit",
     "test": "vitest run --passWithNoTests",
+    "test:e2e": "playwright test",
     "start": "next start"
   },
   "dependencies": {
@@ -21,6 +22,7 @@
     "tailwind-merge": "^3.5.0"
   },
   "devDependencies": {
+    "@playwright/test": "^1.58.2",
     "@tailwindcss/postcss": "^4.0.0",
     "@types/node": "^22.0.0",
     "@types/react": "^19.0.0",