I‘ve already attended the graduation ceremony. But the remaining suggested quest still shows the "【Olvia Academy】 Graduation with Honor" as not completed. I have talked with Justin Batarlli, and have typed Olvium Frontia! in the general chat window in front of him, but the quest is still not completed.

If you open the academy UI, right at the top, it says Graduation: 2026-2-18 20:00 - 2026-4-15 21:00.

As we have not yet gotten there, you can't graduate yet.

I've completed all the quests but don't have the graduation quest. I know it will be on the 2/18 date, but don't have the quest... I see it is unaccepted, yet I did talk to Justin... because the npc's directed me to talk to him. He didn't start the quest for me.

Yes, as the quest is not acceptable until the graduation date is reached. As you can see in the image, the quest also says "Unaccepted" because it cannot be at the time.