So, the original Soul traits are stick around. Without them, the tree would die. Their souls can't be destroyed, only be inherited.

The first DETERMINATION Soul did indeed pass. But, his Soul didn't. It became the Soul of the Scarlet King, thus making him the embodiment of DETERMINATION and one of the more powerful deities around. When he dies, 682 will inherit the Soul.

The Kindess Soul is now the Kind Man, a being within the SCP Verse that does little acts of kindess to lessen the pain of those around him. When he dies, Adalyn will get the Soul. If Adalyn is not Alive, it will go to Rosie.

The Integrity Soul is now Mia, who has extremely powerful magic because of this and her powerful father.

The Bravery Soul is now Dr. Placeholder McDoctorate. Since he won't die due to his situation, it is unknown who will inherit the Soul next.

The Perseverance Soul is now Springtrap AKA William Afton, who doesn't even know he has such power. Only time will tell when he unlocks it...

The Patience Soul went to Andre Toulon. He died, but due to the spell, he still has the soul. It is known who it will go to next, and if it will make them immortal too.

And lastly, the Justice Soul was inherited by The Specter, or SCP-4494. If he is to ever die, it will go to Rosie next, and temporarily combine with the Kindness Soul due to her dual-traited nature.