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They should fall off and regrow, but you can hurry it along by lightly pruning and cleaning it up.

https://www.gardeningknowhow.com/ornamental/shrubs/barberry/barberry-shrub-care-tips.htm

I looked up the specs on the plant and it grows about 1.5 feet wide so you can count on the roots being about that width. If your arborvitae is mature, I would space the Orange Rocket at least 2 feet from it.

I suspect they are getting too much water. Trim off the fried looking part and reduce watering but let the hose run slowly next to them so they will be watered deeply but less often. See if they can go three days without water to begin. Eventually once a week should be enough.

When plants are waterlogged, it damages the roots and they can't uptake water. Then the leaves look like they need water but it's because the roots can't deliver, not because the water isn't available.

When watering less often, but deeply, it encourages deep roots, which benefit the plant, especially in your climate.

Plants can change color due to weather, stress, or other environmental factors. Make sure it is getting fertilized in spring. It has low water needs so don't overdo on the water. It prefers full to part sun.

Oddly enough, when looking at images online of Orange Rocket, I saw a few photos that looked like yours and they were ads for a nursery! So the color changes could be normal.