docs: polish public project surface

[saagpatel]

What

• Replaces placeholder README badges with live CI, PyPI, Python, release, and license badges.
• Refreshes release-gate, workflow, and web UI install docs now that PyPI publishing is active.
• Tightens contributor and security docs for public users.

Why

• The project is now public and published on PyPI, so first-time visitors should see current trust signals and accurate release guidance.

How

• Keeps the change docs-only, with a distribution policy test guarding the public install and badge copy.
• Leaves release mechanics unchanged; this only updates public-facing documentation.

Testing

• ruff check src/ tests/
• python3 -m pytest tests/test_distribution_policy.py -q -p no:cacheprovider
• python3 -m pytest -q -p no:cacheprovider

Performance Impact

• None expected; docs/test-only change.

Risk / Notes

• Repository homepage was also set to the PyPI project page in GitHub metadata.