This idea is being posted as the part of Maintain attachments and relationship classes when using the Project tool that has not been implemented. ArcGIS Pro 2.5 (January 2020) will add Maintain Attachments (Environment setting)—Geoprocessing | ArcGIS Desktop to the Project tool.
Please vote here and add your use case in the Comments if you have workflows requiring the Project tool (or GP tools other than Copy which does currently maintain relationship classes) to maintain relationship classes.
Thank you.
