If I attack an open battlefield with an assault unit, then my opponent's ambush unit, does my unit become assault?

Yes, your unit gains the Assault bonus.

Here is the breakdown of why this happens based on the rules:

1. Moving to the Battlefield

When you move your unit to an open battlefield, you initiate a Showdown. At this stage, because there is no opposing unit, there is no Combat, and your unit does not have the "Attacker" designation. Therefore, the Assault ability is currently inactive.

2. Opponent plays an Ambush unit

When your opponent plays a unit via Ambush, they are reacting to the ongoing Showdown. Because your units are already present at that battlefield, it is a valid location for them to play their unit as a [Reaction].

3. Transition to Combat

Once the opponent's unit enters the battlefield, there are now units controlled by two different players at the same location. This causes the Showdown to transition into a Combat.

• According to Rule 458, when a Combat opens, the player who applied the "Contested" status (you) gains the Attacker designation.
• Your units present at the battlefield receive the Attacker designation.

4. Assault Becomes Active

According to Rule 807.1.c, Assault is functionally short for: "While I am an attacker, I have +X [M]." Since your unit now holds the Attacker designation due to the Combat, the condition for your Assault ability is met, and the bonus is applied.

Note: This is based on the interaction between movement, showdown/combat transitions, and the Assault keyword (Rule 807).