MVP 1.4: Strengthen tests and code

[Boxuan-Matty-Lin]

Background

Phase 1 is stable. Now add missing tests, clean up code, and update docs to avoid carrying tech debt.

Acceptance Criteria

• Unit test coverage: statements and lines ≥ 90% exclude shad/cn UI.
• Smoke tests pass: amount input, rate refresh, error message, a11y alert.
• CI checks are green. Blocking merge on failures.
• No flaky tests. pnpm test:ci runs stable twice.
• Lint and type checks are clean.
• README updated with steps and examples.

Note: Bug fixes and tests only, no new features.