refactor: rewrite e2e tests for clarity and correctness

[Bentlybro]

What

Rewrote the e2e test suite — the old one was broken (login test failing because registration auto-logs you in 😂).

Changes

• Fix the actual bug: Remove redundant login test that fails after registration auto-authenticates
• Modular structure: Separate client class, individual test functions with clear names
• Better output: Shows exactly what passed/failed and why
• Smart CI handling: Detects test-key OpenAI key and skips moderation tests automatically
• Actually runs all tests: Some test functions were defined but never called
• Early exit: Stops if critical setup fails instead of running useless tests

Before

..F..
4/5 tests passed
❌ Some E2E tests failed!

After

▸ Platform Core
  ✓ health check
  ✓ register + auto-login
  ✓ create project
  ✓ get API key

▸ Moderation API (skipped — no OpenAI key)

4/4 tests passed
✅ All tests passed!