It keeps launching the TriaQuaedam quest only now without the prerequisites. Do I have to start the game again for the patch to work?
With the new update's bugfix, TriaQuaedam should only trigger assuming you've done The Grind (Gracie's final event) & A Soldier's Sacrifice (which should trigger only if you chose the netori path).
In your save, did A Soldier's Sacrifice trigger (which shouldn't if you're on Isabel Friendship path) still?
You might wanna load up a save prior to that event to see if the pre-requisites work properly from that point onwards.
But probably best way to test it properly (or if you don't have save prior to A Soldier's Sacrifice event to load) would be restart the game fresh and see if the problem persists.
If the problem persists, then contact
HopesGaming & TechSupport in Hopes' Discord server (in Bug Reporting channel).