"When the final level of this item is reached, there's a 10% chance the skill Shadow Stars or Assassinate will level up by 1."

Could you check if this actually works in-game?

Two parts. The original had no set bonus for Reverse items (no set-item system in this version), so no set effect is correct. The final-level effect you quoted did NOT work, and it does now: when a Reverse or Timeless item reaches its final level there's a 10% chance it awakens its hidden skill bonus (+1). The level-up line names the skill, and the bonus applies while worn, up to the skill's master level.