Is experience per player or per unit?

XP (Experience) is a resource accrued by players, not by individual units.

According to Rule 729, XP is a resource that is accrued, spent, or otherwise modified by players through the course of play, and the amount of XP a player has is public information.

While certain cards may have abilities that trigger based on how much XP you have (which is often referred to as "Level"), and some cards (like Kha'Zix, Voidreaver) may instruct you to gain XP, it is a global resource tracked on the player, not on specific units.