Add fake payment lifecycle API

[FrancisPhan0105]

/claim #1

Summary

• add fake payment records to the shared in-memory database
• add send/list/get/complete/cancel/fail payment routes with request/response schemas
• add idempotency-key replay protection and terminal status transition guards
• document the fake payments API and add route tests

Verification

• npx --yes bun test
• npx --yes bun run build
• npx --yes tsc --noEmit
• ./node_modules/.bin/biome check lib/db/db-client.ts lib/db/schema.ts lib/middleware/with-db.ts lib/payments/schemas.ts routes/payments/send.ts routes/payments/list.ts routes/payments/get.ts routes/payments/complete.ts routes/payments/cancel.ts routes/payments/fail.ts tests/routes/payments.test.ts README.md package.json
• git diff --check