How does scoring work in Riftbound, particularly regarding holding and conquering battlefields?

Ruling: You gain points in two ways: (1) beginning your turn with control of a battlefield gives you a "Hold" point for each battlefield controlled, or (2) ending a showdown with a unit present at a battlefield you do not control (and haven't scored at this turn) gives you a "Conquer" point. Each battlefield can only be scored once per turn.

Sequence:

• Hold points are awarded at the start of your turn for each battlefield you control
• Conquer points are awarded when you end a showdown with a unit at an opponent's battlefield (that you haven't scored at yet)
• You can score multiple points in one turn by holding one battlefield and conquering another

Nuances:

• The final game point (8th point in 1v1) has special rules: if you conquer at 7 points and have scored at every battlefield this turn, you get the victory point; otherwise you score a draw from your main deck
• Battlefield effects apply to both players regardless of who chose the battlefield