This session is not valid for use with the REST API" Error When Using client_credentials Grant Type in Postman

When using the client_credentials OAuth grant type in Postman to call a custom Apex REST endpoint, a "401 Unauthorized — This session is not valid for use with the REST API" error may occur even when an access token is successfully obtained. This error occurs because the Connected App configured for the client_credentials grant type is missing the "Managed user data via APIs (API)" OAuth scope. Without this scope, access tokens generated via the client_credentials flow are not authorized to call REST API endpoints, including custom Apex REST classes at /services/apexrest/.

Screenshot showing a 401 Unauthorized error response in Postman when calling a custom Apex REST endpoint. The response body displays: This session is not valid for use with the REST API.