I have a weird situation at Goertzel's lab: picked up the empty vial, used it on the painting, but the vial is still empty. However, when I try to get more blood it says
"I don't need anymore of that blood" or something like that.
Hm, ok thanks for reporting and sorry about that!
The vial of blood is added and often goes to page 2 of the inventory, if you haven't yet checked there.
If you still have issues here is a walkthrough of the entire game: https://www.youtube.com/watch?v=aJz-YbBpRi8&t=4859s