Add retry-safe fake payment API

[mg272011]

/claim #1

Summary

• adds fake payment records to the in-memory zod/zustand store
• adds send/list/get/complete/cancel payment routes with Winterspec schemas
• supports idempotency keys for retry-safe fake payment sends
• documents endpoint usage and adds route coverage

Verification

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