refactor: move Playwright tests to tests/e2e/ with proper conftest

- Move conftest_playwright.py to tests/e2e/conftest.py for proper pytest discovery
- Move test_playwright_server.py to tests/e2e/
- Server fixture starts FastAPI with uvicorn for isolated E2E testing

tests/e2e/test_playwright_server.py

@@ -9,14 +9,10 @@ This test file verifies that:
 
 from __future__ import annotations
 
-import sys
 from pathlib import Path
 
 from playwright.sync_api import expect
 
-# Import the server fixture from conftest_playwright
-sys.path.insert(0, str(Path(__file__).parent))
-
 ARTIFACTS = Path("tests/artifacts")
 ARTIFACTS.mkdir(parents=True, exist_ok=True)