Add fake payment flow

[JPL-Jarvis]

Adds a small fake payment flow on top of the existing in-memory store:

• send a pending fake payment
• replay the same payment when an idempotency key is reused
• list/filter payments
• fetch one payment
• update payment status

/claim #1

Checked locally:

• bun test tests/routes/payments/payment-flow.test.ts
• bun test
• bunx biome check lib/db/schema.ts lib/db/db-client.ts routes/payments tests/routes/payments/payment-flow.test.ts README.md types/dist-bundle.d.ts --write
• bun run build
• bunx tsc --noEmit
• git diff --check