Add fake payments API

[surim0n]

/claim #1

Summary

• Adds fake payment records to the in-memory database schema.
• Adds send, list, get, and terminal status update routes for fake payments.
• Makes send idempotent when an idempotency_key is provided.
• Documents the payment endpoints in the README.

Verification

• bun install --frozen-lockfile
• bun test tests/routes/payments.test.ts
• 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

[surim0n]

Fresh local verification for review:

• bun install --frozen-lockfile -> no changes
• bun test tests/routes/payments.test.ts -> 2 passed
• bun test -> 4 passed
• bunx biome check lib/db/schema.ts lib/db/db-client.ts routes/payments tests/routes/payments.test.ts README.md -> passed
• bun run build -> bundled successfully
• bunx tsc --noEmit -> passed
• git diff --check -> passed

Functional demo path: the payment route test sends a fake payment, lists payments, fetches the created payment, completes it, verifies idempotent send replay with the same idempotency_key, and verifies terminal-status protection so a completed payment cannot be moved again.

This keeps the PR reviewable and avoids pretending a 40-file mega-patch is a personality trait.