Catch terminated coverage on open claims

I'm building on the Daybook API (healthcare billing: payer calls, payer portals, 270/271 eligibility, 276/277 claim status, 835 remits, denials and appeals). Help me build this end to end.

Use case: Catch terminated coverage on open claims
For: RCM and EHR vendors
Outcome: When a patient's coverage changes, your product flags their open claims and visits, and can call the payer to confirm.

What to build:
A coverage watch inside our product: scheduled eligibility checks with POST /v1/eligibility/checks for every patient with an open claim or an upcoming visit, a handler for coverage.changed that flags those claims and visits for the billing team, and a button on the flag that starts a payer call with POST /v1/calls (call_type eligibility) whose call.completed answer is shown on the patient.

How it works:
1. Run eligibility checks for patients with open claims or upcoming visits.
2. A re-check that finds different coverage sends coverage.changed.
3. Flag the patient's open claims and upcoming visits in your product.
4. Where the 271 leaves it unclear, start a payer call with call_type eligibility.

Read these docs first (Markdown):
- https://daybookhealthcare.com/docs/workflows/eligibility.md
- https://daybookhealthcare.com/docs/workflows/payer-calls.md
- https://daybookhealthcare.com/docs/api-reference/eligibility/create-check.md
- https://daybookhealthcare.com/docs/api-reference/calls/create.md
- https://daybookhealthcare.com/docs/webhooks/verifying-signatures.md
- https://daybookhealthcare.com/docs/idempotency-and-errors.md

Endpoints (base https://api.daybookhealthcare.com/v1):
- POST /eligibility/checks: Check eligibility
- POST /calls: Start a call

Webhook events: coverage.changed, eligibility.completed, call.completed

Ground rules:
- Authenticate with the header Authorization: Bearer <key>, the key read from DAYBOOK_API_KEY. sk_test_ keys open a sandbox and sk_live_ keys reach real payers. Never hard-code a key. Details: https://daybookhealthcare.com/docs/authentication.md
- Send an Idempotency-Key on every POST: a fresh UUID per operation, reused only to retry that operation. A key reused with a different body answers 409 idempotency_conflict.
- Verify every webhook signature before trusting the event, answer 2xx at once and do the work after.
- Keep my own ids beside Daybook's, and pass them in metadata where an endpoint takes it.
- Money is integer cents.
- Tests and fixtures use made-up data only: the sample payers bayline, keystone and meridian, NPI 1999999984, member W000000001, claim ids like clm_8Hq2Lm. Never real patient data.
- Use only the fields, endpoints and events in the docs. If something is missing, ask me rather than guess.

Ask me how patients, claims and visits are stored in our product, then propose the flag and where it shows before writing code.