Once Serpent Strike has created a Primal Serpent, the following node named ‘Vicious Strikes’ allows the serpent to heal itself when it hits enemies with a melee strike (according to the wording). The health granted on Primal Serpent melee strike does NOT work. I am unsure if the Attack speed % works.
Of note: I am cheesing the skill by using a spear to summon the serpent, and then changing my weapons to a mace. While I can no longer use the ability Serpent Strike, the Primal Serpent remains and acts appropriately.
Edit note: Removing the skill from the hotbar, adding it back to hotbar, and having the serpent be resummoned resolved the issue.