This issue has been resolved. The second step, Upload Binary, requires the asset's mimeType to be included in the request as part of the Accept header. Doing so resolved the authentication issue.

I am trying to upload assets to AEM Cloud Service using the Asset Upload feature since the Assets HTTP API for creating assets is deprecated. The documentation I am using is here: https://experienceleague.adobe.com/en/docs/experience-manager-cloud-service/content/assets/admin/developer-reference-mat...