Yes, you are required to perform a DAST scan on external endpoints, including third-party APIs that your application integrates with, for the AppExchange Security Review. You must include the DAST scan report in your submission, detailing the scan date, targeted endpoints, and findings.
A passive scan or spider crawl may not be sufficient for a public API that you do not control in the AppExchange Security Review. The review process requires control over the external endpoint, including the ability to place a token in the web app root for testing. If you do not have control over the endpoint, the review may be canceled.
Active scans are required for third-party API scanning to effectively identify vulnerabilities. A spider crawl alone is not sufficient, as it only maps the application structure without simulating real-world attacks.