fix: make test_ping deterministic

[Krish0703-irl]

Description

Updated test_ping to use TestClient as a context manager instead of a global instance. This ensures proper startup/shutdown lifecycle handling and improves test reliability.

Related Issue

Fixes #521

Type of change

• Bug fix
• New feature / enhancement
• Documentation update
• Test addition
• Refactor

Checklist

• I have read CONTRIBUTING.md
• My branch is up to date with main
• I have run pytest -v and all tests pass
• I have not introduced duplicate issues or features
• My PR title follows the format: feat/fix/docs/test: short description
• I have added tests for new features (Level 2 and 3 issues)
• No hardcoded secrets or API keys in my code
• This PR is linked to a GSSoC 2026 issue

Test evidence

pytest tests/test_ping.py -v

============================== test session starts ==============================
...
tests/test_ping.py::test_ping PASSED
======================== 1 passed, 2 warnings in 0.53s =========================fix: make test_ping deterministic