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

Fixes #1

[chatgpt-codex-connector]

💡 Codex Review

Here are some automated review suggestions for this pull request.

Reviewed commit: 8d2039faa6

ℹ️ About Codex in GitHub

Your team has set up Codex to review pull requests in this repo. Reviews are triggered when you

• Open a pull request for review
• Mark a draft as ready
• Comment "@codex review".

If Codex has suggestions, it will comment; otherwise it will react with 👍.

Codex can also answer questions or update the PR. Try commenting "@codex address that feedback".

[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.

[jynbil1]

Quick status check: the Algora claim page for this PR is still pending. This PR has /claim #1, Fixes #1, and the bounty-claim label; I do not see any failing checks. Happy to adjust anything needed for review, merge, or reward.