>>1009739First, are you certain the new rim has the same ERD and drilling pattern (is there an offset?) as the old one?
But yes, it's totally normal for the driveside spokes to be under more tension because the spokes are a bit shorter and have a steeper bracing angle (because the hub flange on that side sits closer to the center of the hub).
Fun fact: there/are were designs that intentionally try to do away with the difference in spoke tensions on sides of a wheel by making the driveside flange extra large.