Add fake payment send API

[SkinnyFatBoy05]

/claim #1

Summary

• add in-memory fake payment records and a sendPayment database action
• add POST /payments/send with generated ids, sent timestamps, and idempotency-key replay protection
• add GET /payments/list with optional recipient filtering and README endpoint notes
• await the existing thing-create test request to remove a race

Verification

• npx.cmd bun install --frozen-lockfile
• npx.cmd biome check .
• npx.cmd bun test
• npx.cmd bun run build
• .\node_modules\.bin\tsc.exe --noEmit