Well its up to final fantasy/square enix if they want the quartz regalia to be added to fh5. They might say no. But i doubt it coming back because in fh4 the licensing deal expired for the quartz regalia in april 2021 i think and it got removed from the festival playlist and forzathon shop in fh4.
So the only way to get the quartz regalia and the quartz regalia type d in Forza Horizon 4 is through auction house.