I have not been a user of Fuji and I only have the 1st generation Z5.
The Nikon terminology is Picture Controls for the color profiles. With the default setup, the Picture Controls are available after pressing the "i" button and selecting in the menu that appears. You can preload profiles on your memory card to use, some are already available (like B/W).
Here is an overview from Nikon
Learn how to make your photos and videos unique looking with the PIcture Control presets that are built into your Nikon digital camera
www.nikonusa.com
There is a software package for creating your own custom profiles, but it is some advanced stuff. Far easier to download profiles at this website:
Nikon picture control editor. The web application lets you view and edit nikon camera styles directly in a web browser. Follow picture control parameters can be modified: custom curve, gamma, sharpness, saturation, hue, etc
nikonpc.com
That is not an official Nikon site though. I have played with some of the film simulation profiles. Personally I still think Nikon Normal profile is the most accurate color to eyesight. But if you expect color to pop, you will want to change to something else.
My first Z-mount lens is a 24-70mm f/4 and I adapted my older F-mount lenses as I slowly have been buying replacements. You may want to give strong consideration to the Z24-120mm f/4 as that was still very new when I was shopping. The closest lens in your Fuji kit to that is the 16-80mm f/4 (considering the 1.5x crop factor of the Fuji compared to the full-frame sensor Z5II).