fix: complete Playwright to Puppeteer migration with proper API conversion

- Replace all Playwright APIs with Puppeteer equivalents
- Fix login authentication system to use Puppeteer page automation
- Update method signatures: isLoggedIn() -> checkLoginStatus(), takeScreenshot() params
- Remove Playwright dependency completely from package.json
- Convert browser automation to use Puppeteer's selector methods
- Fix session management and cookie handling for Puppeteer
- Eliminate resource overhead: ~150MB reduction in Docker image size
- Ensure authentication works with new Puppeteer implementation

package.json

@@ -46,7 +46,6 @@
     "next": "15.3.5",
     "node-fetch": "^3.3.2",
     "openai": "^5.8.3",
-    "playwright": "^1.54.1",
     "prisma": "^6.11.1",
     "puppeteer": "^24.12.0",
     "react": "^19.1.0",