Proposal: add test infrastructure (pytest + vitest) and CI workflow

[mykolakhy]

CONTRIBUTING.md mentions the project doesn't have much test coverage yet ("we're working on it as we test the idea"). Right now there's test_setup.py, which is a manual smoke-test script (print-based, no assertions/framework) rather than an automated test suite, and no CI workflow to run it.

I'd like to help improve this, starting small:

1. Add pytest config (pytest.ini/conftest.py) for the Python backend (database.py, web-app/api/*.py)
2. Add vitest + React Testing Library config for the web-app/src React components
3. Add a GitHub Actions workflow to run both suites on PRs
4. Follow up with small, focused PRs adding tests module-by-module (starting with database.py)

Before putting time into this — is this something the maintainers would want, and is there a preferred testing approach already in mind? Happy to open a PR for the infra piece first if useful.