Improve Playwright Test Coverage and Stability to Eliminate Manual UI Testing

[Spiral-Memory]

As an EmbeddedChat developer

I need to:
Strengthen and expand Playwright test coverage for PR-related flows and UI interactions.

So That:
We can rely on automated tests instead of manually testing changes locally or through the UI, improving reliability and development speed.

Acceptance Criteria

• Tests are stable, deterministic, and do not fail due to timing or flaky selectors
• Mocking or test fixtures are used where appropriate to avoid dependency on external services
• Tests run successfully in CI without requiring manual setup
• Clear failure messages are provided to help debug issues quickly
• Test execution time is optimized and does not significantly slow down CI pipelines