With any of these modes, you have to be aware that the camera is not actually 'intelligent', nor particularly 'smart'. You have to give it some good clues as you what you're after, and also try your best to follow it yourself.
It's not a bad camera & it's not a bad lens, but it's not …erm …expensive enough to have the latest & smartest eye-tracking & faster than you can blink auto-focus. I have similar but not identical. I have the older D5500 & the even more of a stretch 18-300mm, but I'm going to guess they're similar enough to be a reasonable comparison.
I'm going to assume for this type of shot you're at or near 300mm all the time, which is where it's going to be at its slowest & least forgiving, with an f/6.3 aperture [same as mine]. The smaller your maximum aperture, the slower the focussing will be. In poor light sometimes that can be more 'point & hope' than 'point & shoot'. In decent daylight though, even overcast, it ought to be fast enough to mainly keep up. Your example shot seems predominantly backlit, which I don't think is going to make it any easier.
Most times I just open the aperture right up at minimum zoom, so the camera will always keep it as open as it can wherever you set the zoom to. One less thing to think about. [This doesn't affect the speed of auto-focus, I just like to keep my ISO down & my DoF shallow.] I actually use ISO as much as I can to ball-park my exposure, trying to keep it as fast as possible without running out of headroom & tend to only close down aperture if I run out of compensation on ISO. In Aperture Mode you can set ISO on the Fn button + jog-wheel. [Fn is at the front left of the camera, just under the flash pop-up… & yes, that can be a bit irritating until you get a feel for it;)
After that, it's a case of trying to keep up with your subject. I sometimes use Continuous focus [AF-C] with 3D tracking. Other times, I'll keep it on single point & just do my best to keep up myself. tbh, over a few years I've got better at that than trying to get the camera to be smart enough to know what I actually want all the time.
If you're going to trust to the continuous tracking, I think you'll find that the 3D tracking will be a lot better than the full Auto-area AF. That will force you to hit your subject centre-frame at first half-press, but will then follow reasonably well, so long as you can keep your subject within the 'focus box' marked area towards the centre. If it goes outside, it will lose it.
The other thing is you might have to take 6 shots, none of which work this time… but next time you might nail it. I throw out a whole lot more than I keep. I cull in camera if I know I didn't get the shot then cull again heavily when I have them in the computer. No point keeping the ones that have no hope of being keepers.