Tracking dogs has also been hit and miss with DJI (and more miss than hit).
The way DJI explained Active Track 2.0 (and I assume 3 is similar) is that it is pre-programmed to recognize different objects (DJI has said 16 of them in Active Track 2.0, although I don't know that anyone has seen a list of what the 16 are, although we know people, cars and boats are included) and has different algorithms on how to track those programmed items.
I believe, outside of those items, you need really good contrast. I've seen some video of an all white dog tracked decently on green grass. You've got a multi-colored dog, and the shots against the brown fence aren't going to work. Thought you might have better luck against the grass, but didn't seem like it. Dogs are hard, because as they move, their shapes are always different. Add in a multi-colored dog where the color pattern changes with every movement, and it I don't think you'll have too much success.
As already noted here, you probably will have some better luck if you can get a solid color high-contrast vest on the dog.