Ledger sync: finish the payments integration with paging, bad records, retries and safe payouts

Context

Welcome to finance engineering. ledgersync/ imports charges from our payments provider and sends payouts. Someone started it and moved teams: it works on a quiet account and nowhere else. The provider's API is in docs/API.md; our rules are in README.md. Read both before you write code.

You have 50 minutes. The checks are graded one by one, so each part you get working counts even if the rest is not done. It is open book: the docs, the code and the Python docs are all fair game.

IN-1: Only the first page is imported

Acceptance criteria

• sync_charges reads every page and imports every succeeded charge once.

IN-2: One bad record stops the import

Acceptance criteria

• Malformed charges are skipped and counted; the rest still import.

IN-3: Any error stops the import

Acceptance criteria

• Requests are retried as the README describes: Retry-After for 429, one second for 500 and unreadable bodies, at most four attempts, no retry for 400.
• When a request still fails, sync_charges returns "failed" and keeps what it imported.

IN-4: A retried payout paid twice

Acceptance criteria

• pay_out never makes two payouts for one call, however many retries it takes, and returns "failed" instead of raising.

Notes

• Run pytest tests/visible. Two tests fail on the current code.
• Do not edit ledgersync/session.py or fakepay/: the checks drive them.
• Practice task in the format reported for Stripe's Integration round: build against a provided API inside an unfamiliar repo. Original StackYard code and a made-up API, not the actual question; not affiliated with Stripe.