Add fake payment sending API

[jynbil1]

Adds a fake payment API for #1.

What changed:

• Adds payment persistence to the in-memory db schema/client.
• Adds POST /payments/send with currency normalization and idempotency-key deduplication.
• Adds GET /payments/list and GET /payments/get.
• Adds POST /payments/update-status for payment lifecycle updates.
• Documents the payment endpoints in the README.
• Adds route tests for send, list, get, idempotent resend, and status update behavior.

Verification:

• bun test tests/routes/payments/send.test.ts
• winterspec bundle -o dist/bundle.js
• tsc --noEmit
• biome check README.md lib/db/schema.ts lib/db/db-client.ts routes/payments/update-status.ts tests/routes/payments/send.test.ts

/claim #1

[chatgpt-codex-connector]

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[jynbil1]

Fixed the default currency issue from the automated review and added a regression test for requests that omit currency. Re-ran Winterspec bundling and tsc --noEmit successfully.

[jynbil1]

Added /claim #1 to the PR body so this PR is explicitly tied to the bounty issue.