When an ability says once per turn, does that mean once per player turn, or does turn 10 mean both players' turns?

"Once per turn" in Riftbound refers to once per player's turn, not once per turn cycle. So turn 10 means you can use the ability on your own turn and your opponent can use the same ability on their turn — each player gets one use per their respective turn.

This is confirmed in FAQ #7963: "Once per turn" means once per player's turn, not once per turn cycle, and there is no "half turn" system in Riftbound. So if both players control a copy of the same card with "once per turn," each can activate it on their own turn independently.