Add fake payment lifecycle API

[justusaugust]

Summary

• add fake payment records to the existing zod/zustand database
• add send/list/get/complete/cancel payment routes with idempotency-key replay support
• cover creation, replay, filtering, lookup, completion, cancellation, and terminal-state guards with Bun route tests

/claim #1

Verification

• bun test
• bunx tsc --noEmit
• bunx biome check lib/db/db-client.ts lib/db/schema.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 README.md
• bun run build
• git diff --check

AI-assisted with Codex; I reviewed the implementation and local verification output.