Things I noticed with the new harpoon mechanics:
If the harpooned target is coming to you, you will not consume stamina
If the harpooned target is trying to get away from you, it consumes stamina. The stamina consumption is probably based on the size of the target and burns through your stamina at a much faster rate than before, since I tried harpooning deers just for the heck of it.

I'd recommend harpooning a serpent when its close to the shore, not as soon as you see one. On my serpent hunts, it usually requires me to harpoon it once or twice