docs(time): fix response examples

[Sean-Kenneth-Doherty]

Summary

• add the day_of_week field to the Time server response examples
• fix the conversion example so the New York to Tokyo datetime values and time_difference are internally consistent
• add a regression test that parses the README response JSON blocks and compares them with frozen TimeServer output

Validation

Run from src/time:

• uv run pytest
• uv run ruff check .

Local result: 39 passed, ruff clean.