refactor: improve integration tests stability

- Replace inline StepVerifier assertions with AtomicReference pattern for better testability
- Add assertWith() usage for cleaner assertion blocks in async tests
- Simplify reactive chains using doOnNext() and thenReturn() patterns
- Remove unnecessary Thread.sleep() from elicitation handler
- Improve variable naming (rootsRef → toolsRef) for clarity
- Update timeout error message assertions to be more specific
- Clean up code formatting and remove redundant comments

Signed-off-by: Christian Tzolov <christian.tzolov@broadcom.com>