I have tried the following with success in the flow itself, but the Project Owner field remains unchanged.
Adding a step to add new resource to Resource Pool via the EnterpriseResource uri (_api/ProjectServer/EnterpriseResource) and then adding them successfully to the Resource center via Email in the body). [This was to address the issue in the post referenced above].
Adding a step to add the individual directly to the SPO/Project Online site as PWA is using SP permissions, and this too happened successfully. (I added them to a SP only group, not one of the default PWA groups if this makes a difference).
Querying their SP UserID from the above step and then trying two different ways to change the Owner of the project with the SP UserID.
Creating a SP request to _api/ProjectServer/Projects('id here')/Draft and patching in the 'Id' string to the 'OwnerId'.
Creating a SP request directly to the Owner endpoint like _api/ProjectServer/Projects('id here')/Owner, and using the 'LoginName' parameter.
All steps conclude successfully, but none actually update the Project Owner. Is there something else I am missing?
Looking through you post here it seems like you are doing everything correctly. I'm not 100% sure why you are encountering this issue. I would recommend opening a ticket with Microsoft Support. I'll include a link below on how to do so. If any other communities members have any ideas feel free to chime in.