Add fake payment API

[thepianistdirector]

/claim #1

Summary

• Add an in-memory fake payment record model and DB helpers.
• Add send, list, get, complete, and cancel payment routes with validation.
• Add idempotency-key replay protection for retry-safe sends and status-transition guards.
• Document the payment API in the README and cover the lifecycle with route tests.

Validation

• npx.cmd bun test
• .\node_modules\.bin\biome.exe check README.md lib\db\schema.ts lib\db\db-client.ts routes\payments\send.ts routes\payments\list.ts routes\payments\get.ts routes\payments\complete.ts routes\payments\cancel.ts tests\routes\payments.test.ts
• .\node_modules\.bin\tsc.exe --noEmit
• npx.cmd bun run build
• git diff --check

Transparency: AI-assisted with Codex; I reviewed the diff and kept the change scoped to the fake payment API.