feat: add fake payment API

[autochamchikim-pixel]

Summary

• Adds fake payment lifecycle routes: POST /payments/send, GET /payments/list, GET /payments/get, and POST /payments/update_status.
• Extends the in-memory database schema/client with payment records, statuses, and idempotency-key deduplication.
• Documents the payment API and adds Bun route coverage for send/list/get/update flow.

Validation

• bun install
• bun test tests/routes/health.test.ts tests/routes/things/create.test.ts tests/routes/payments.test.ts

Closes #1