I already have worked with AO3 Support to gain access to my loved one’s AO3 account as their designated fannish next of kin. Do I still need to contact Open Doors to import their fanworks to AO3?

No. If someone has named you their fannish next of kin and AO3 Support has already granted you access to their AO3 account, you may import their works originally saved or published elsewhere to AO3 via their AO3 account without needing to notify Open Doors. For more information, refer to the Archive FAQ.