Continue the existing equipment-rental contract project from delivered commit b3a4147a74e84445ef3f69c1a15ee797ce54ba2f in https://github.com/identity-md-launches/launch-1988-kkk.

This iteration tests maintenance of an existing codebase. Deliver source and local tests only. Keep the existing rental rules and accounting protections. Do not deploy to a public blockchain, launch a traded token, create a pool or publish a website.

1. Harden administrator fee-withdrawal retries. The current withdrawFees(to, amount) permits the same application request to pay twice when submitted as separate transactions with different nonces: earn 10 tokens of cancellation fees, withdraw 5, then repeat the call and another 5 is paid. Customer deposits remain protected, but the request itself is not deduplicated. Add a caller-supplied unique withdrawal request ID and store a durable result including recipient and amount. Reusing the ID must never move funds again; conflicting parameters must be rejected. Old completed IDs must remain protected across admin handover. A different ID must still permit a legitimate new withdrawal. Failed transfers must not consume an ID or reduce accrued fees. Explain the chosen replay response and provide a lookup/event for recovery.

2. Correct the integration guide's uncertain-transaction recovery. Distinguish rebroadcasting the identical signed transaction from submitting a new transaction for the same application request. Do not use a mutable balance alone to infer that an earlier withdrawal succeeded. Explain that withdrawRefund withdraws the beneficiary's current aggregate credit: if a new reservation settles between calls, a later call may withdraw that new credit. Each credit must still be paid only once. Document transaction hash, sender nonce, receipt and event reconciliation for this case.

3. Add ItemCheckedOut to the backend item-state projection. Keep it consistent with reservation status and getItem().

4. Correct test counts and regenerate TEST-RESULTS.md from the final delivered tree. The previous tree contains 71 tests, although its summary says 64. Preserve existing coverage, update affected ABI/event assertions, and add regressions for the fee retry, conflicting request payload, failed-transfer rollback, admin handover, and refund recovery with intervening new credit. Run build, formatting, tests and the Anvil demo. State exact tool versions and checks actually run.

Explain the changes and any interface compatibility implications. Identify any requirement you could not complete. Do not add unrelated features or redesign the escrow.