feat: Add Playwright automated testing for authentication flow

- Install Playwright for automated browser testing
- Create comprehensive auth flow test script with screenshots
- Verify authentication fixes prevent flashing and redirect loops
- Generate visual proof that unified auth system works correctly

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

package-lock.json

@@ -28,6 +28,7 @@
         "cheerio": "^1.1.0",
         "dotenv": "^17.1.0",
         "node-cron": "^4.2.0",
+        "playwright": "^1.54.1",
         "qrcode": "^1.5.4",
         "ramda": "^0.31.3",
         "react": "^19.1.0",
@@ -9293,6 +9294,50 @@
         "node": ">=16.20.0"
       }
     },
+    "node_modules/playwright": {
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+      "resolved": "https://registry.npmjs.org/playwright/-/playwright-1.54.1.tgz",
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+      "license": "Apache-2.0",
+      "dependencies": {
+        "playwright-core": "1.54.1"
+      },
+      "bin": {
+        "playwright": "cli.js"
+      },
+      "engines": {
+        "node": ">=18"
+      },
+      "optionalDependencies": {
+        "fsevents": "2.3.2"
+      }
+    },
+    "node_modules/playwright-core": {
+      "version": "1.54.1",
+      "resolved": "https://registry.npmjs.org/playwright-core/-/playwright-core-1.54.1.tgz",
+      "integrity": "sha512-Nbjs2zjj0htNhzgiy5wu+3w09YetDx5pkrpI/kZotDlDUaYk0HVA5xrBVPdow4SAUIlhgKcJeJg4GRKW6xHusA==",
+      "license": "Apache-2.0",
+      "bin": {
+        "playwright-core": "cli.js"
+      },
+      "engines": {
+        "node": ">=18"
+      }
+    },
+    "node_modules/playwright/node_modules/fsevents": {
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+      "resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
+      "integrity": "sha512-xiqMQR4xAeHTuB9uWm+fFRcIOgKBMiOBP+eXiyT7jsgVCq1bkVygt00oASowB7EdtpOHaaPgKt812P9ab+DDKA==",
+      "hasInstallScript": true,
+      "license": "MIT",
+      "optional": true,
+      "os": [
+        "darwin"
+      ],
+      "engines": {
+        "node": "^8.16.0 || ^10.6.0 || >=11.0.0"
+      }
+    },
     "node_modules/pngjs": {
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