From the photo of your f2 settings:
You have AF-On=Only, so the half press shutter doesn't AF -- good.
The F1 is good. It can be used for an autofocus handoff to 3D, or as an alternate AF-On directly choosing 3D instead of your current AF mode.
But the AF-On button should be set to "AF-ON", not "Auto Area+AF-ON". That way, you can pick any of the AF box sizes, like Wide Area Small or Wide Area Large, or the custom sized C1 or C2 AF boxes. Your AF-On setting will override the i-menu AF choice, which isn't helpful.
I rarely use Auto Area AF. I want to limit the AF to smaller areas in the scene. Steve Perry at backcountrygallery.com likes Auto Area for bird detect shooting, but I think that's at least partly due to his expert choosing of a low distraction background, for a better composition and reliable autofocus. For me, Auto Area is just too unpredictable.
So change AF-On to be the standard "AF-ON". Now you can use the i-menu or other methods to pick an appropriate autofocus box size. If the subject is actively moving around the scene, you can hand off a detected subject by releasing AF-On and immediately pressing F1 to track it in 3D.
In this context, I would also like to refer you to a very useful video by Steve Perry.
The "Cycle AF Area" feature was introduced with Nikon Z8 firmware 2.0 and Nikon Z9 firmware 5.0, and it has completely overhauled the way of working with AF areas.
This allows you to switch between AF fields with a simple push of a button, for example with the video button, which is extremely fast and intuitive, especially if you have previously limited the AF fields to those that are essential for you.
Steve Perry's video guides are highly recommended and helpful, and for me personally, they are much more to the point than Hudson Henry's guides, which are also good, but he digresses more often, unnecessarily prolonging many of his video guides.
I studied Steve Perry's guides for the Z8/Z9, among other things, weeks before purchasing my Z8 and was able to use the Z8 at a high level right away.
Immediately after purchasing the Z8 body, I had an important event to photograph with it and was already so familiar with the essential features and optimal configuration that I had the camera under control right away.
It helped me a lot, especially as a orientation for finding the optimal camera configuration for me.
Cycle AF on the video button, or another button depending on your preference, is one of these very helpful and effective configurations that allows extremely fast access/fast switch to the AF boxes used.
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Another Steve Perry tip that I also found extremely helpful and effective is a Wide Area Custom Box with dimensions of 1x1 for very precise subject detection.
This essentially gives you an AF box the same size as a Single Point AF, with the difference that this one works as a Wide Area Box with subject detection, which isn't the case with the classic Single Point AF box.
In difficult, cluttered situations or scenes, you can use it to apply subject/face/eye recognition/detection very precisely and then continue working in 3D via handoff.
It helped me a lot with subject recognition when photographing events with multiple people, many subjects, faces, and eyes.
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The last really good tip, at least if you do action/wildlife/sports photography frequently, is the "Emergency Action Button".
One of the things that hasn't really evolved with new technology is the ability to react incredibly quickly to significant need of changes in shutter speed.
For example, if I'm photographing a bird that's moving very little, and I'm working with shutter speeds appropriate for the low movement rate to keep my ISO low, and suddenly action occurs, then adjusting the shutter settings via the dial(s) usually takes far too long.
With this method, via the Recall Shooting function, you have your action settings for BiF shots at the touch of a button.