Add coverage badge to README

Currently the project enforces coverage thresholds in CI and detects regressions on pull requests, but there is no at-a-glance signal of the project's overall coverage level. Adding a badge to README.md would make the current state visible to contributors and maintainers without having to dig into CI logs.

Beyond visibility, a coverage badge implies integration with a coverage tracking service — which unlocks a secondary benefit: a public, queryable source of the main baseline. This would allow tooling like a pre-push regression check to fetch the current coverage numbers automatically, with no setup required from contributors.

Acceptance criteria:
- README.md shows a coverage badge that reflects the current main coverage
- The badge updates automatically on each merge to main
- The underlying service exposes a public API that can be queried without authentication (to enable future pre-push tooling)

Possible approach: integrate with a coverage tracking service such as [Codecov](https://codecov.io/), which is free for open source and meets all three criteria above.

Start with README.md and inspect the existing CI configuration that enforces coverage thresholds. Evaluate Codecov or a similar service against the stated public-API and automatic-update requirements, then verify that the README badge reflects main coverage and updates after merges.

Written by the indexing model from the issue text.