My enemy enters open battlefield with their unit, while in showdown I cast Zenith Blade to move my unit onto the battlefield that my enemy just moved their unit. Which unit is the attacker, mine or the enemy's?

Based on the rules and the specific interaction you described, here is the ruling:

The Ruling

Your opponent is the Attacker, and you are the Defender.

According to RiftJudge FAQ #2853 and Rule 459.2.b.1, the Attacker is the player whose unit(s) first applied the Contested status to the battlefield. Because your opponent moved their unit into the empty battlefield first, they applied the Contested status and became the Attacker. When you subsequently used Zenith Blade to move your unit to that same battlefield, you became the Defender.

Sequence of Events

1. Opponent's Move: Your opponent moves their unit into an empty battlefield. The battlefield becomes Contested, and an open showdown begins. Your opponent is designated as the Attacker.
2. Your Response: During the showdown, you play Zenith Blade.
3. Zenith Blade Resolution: The spell resolves: you stun the enemy unit and move your unit to that battlefield.
4. Combat Designation: Because units from both players are now present, a combat showdown is created.
   • Attacker: Your opponent (the player who first applied the Contested status).
   • Defender: You (the player who moved in second).
5. Combat Begins: After the initial showdown completes, combat begins. Your opponent (the Attacker) gains Focus, and any "When I attack" or "When I defend" triggered abilities will resolve at this time.

This is based on the established mechanics for Contested status and combat designations as documented in the Riftbound rules and FAQs (specifically FAQ #2853 and #9032).