once i get the vase from underwater and escape the paramilitary boat, i swim to the shore (passing under the bridge then following the coast) but once i'm on the shore marker nothing happens and this mission does not finish (even if i go and see the old man who gave it to me)
I can take a look at this if you tell me exactly how the old man is called and what he says when you talk to him again.
Quest wasn't broken for me (GG version). But marker did got updated after getting to shore (there, I killed a few more bandits), and it pointed to vase owner.
The npc name is Old Alberto, and the dialog is the same as the one you get just after picking the vase quest and before going to the bandits.