"I used to use a Fujifilm camera [or fill in another brand, I get this question in all forms]. The out-of-camera JPEGs on my new Nikon Z camera don't look as good as I'm used to. How do I fix that?"
Fujifilm and Canon both tend to use double hue shifts in their defaults. Greens and reds both move towards yellow (that's opposite directions on the hue wheel, which is why we call it a double hue shift). Fujifilm also adds saturation and contrast.
Every camera maker has a department entirely devoted to tweaking default (and other possible settings) to produce pleasing images. The problem is that every camera maker has a different definition of what pleasing is. Moreover, so do most image viewers. The more we've been saturated with images everywhere, the more it takes for an image to stand out. Increased color saturation, shifted tones, and higher contrast are all things that help do that.
Nikon has always tended towards a more neutral rendering. Indeed, the Neutral Picture Control on the Nikon EXPEED-based cameras is about as neutral as it comes in terms of JPEG rendering, particularly if the white balance was set properly. Nikon more recently added an Auto Picture Control, which attempts to do scene recognition: a portrait, landscape, and street image all taken in the same light will have differing parameter settings, though not as intense as the Portrait or Landscape or Vivid Picture Controls would produce. Auto is sort of a nod towards "hey, the others are goosing their pixels, maybe we should too," but without a big step in any direction.
The problem I have with answering the exact question—how do I make my Nikon JPEGs look like my Fujifilm JPEGs—is that most people can't tell me what it is about those JPEGs that they're reacting to. If I knew that, I could tell you what to set to (mostly) duplicate that.
Note that with the latest Z6 II and Z7 II firmware (1.30), you can start to do the one thing that you couldn't used to do with Nikon Picture Controls: something similar to a double hue shift. Nikon's new Portrait impression balance menu item allows you shift skin tone hues one direction, but you can shift overall color the opposite direction with the Hue parameter in the Picture Control, or with the White balance color parameter shifting. I don't find Nikon's integration of all this particularly good. These things all need to be driven together, but they're wildly separated in the menu system.
If you tell me specifically what it is you miss in a Nikon JPEG versus what you like in a Fujifilm JPEG, I'm pretty sure I can dial you in to what you want. But most of you can't, so it becomes a long trial-and-error thing. Contrast is impacted on Nikon EXPEED-based cameras by at least five parameters you can set, and color is impacted by at least another five. But if you don't specifically set any of those, well, you'll get Nikon's default choice.
"I’m wondering if you could work up an article to discuss photographing fast action on a modern mirrorless camera please."
The questioner also asked about viewfinders and shutters and mirror flapping, and a whole host of things that are different between a DSLR and a mirrorless camera.
Let me cut to the chase: the simple answer is that you perform fast action photography on a mirrorless camera much the same way you do as on a DSLR. Moreover, the further back your DSLR was made, the more likely that current mirrorless cameras, such as the Z6 II and Z7 II, will surpass it.
With DSLRs the optical finder is the thing that attracts everyone: you see in real time what the lens is seeing (via a mirror and prism system). We have two elements that define how "responsive" the DSLR really is. First, the focus system. The DSLR focus systems operate at a higher frequency (speed) than do the mirrorless cameras, but that comes with drawbacks. You have to look specifically at a whole bunch of parameters that intersect with that speed. For instance, mirror flip and blackout time: the focus system only gets information when the mirror is down. Moreover, there are limits on where focus can be performed and how good it is, and these are defined by a whole host of variable things, including both geometry and the spherical aberration of a fast lens.
The big issue with DSLRs is that they are mechanical devices. In the Nikon system, not only do we have two mirrors and a shutter that are mechanical, but we also have mechanical aperture mechanisms in most lenses. At "affordable" levels, how fast those things can operate has a real limit. There's a reason why the D6 has very low viewfinder blackout time: you're paying more for the mirror flipping mechanism, among other things. Mechanical systems aren't always repeatably precise, either. To make them more precise is once again something that takes money to solve.
Early on in the mirrorless era, those cameras had some significant "lag" and "performance" issues. One was mechanical: because the shutter was open for composing, the shutter tended to double-clutch (close open close open) for each image. I won't go into the details of why this was done, because we're mostly over it with current systems (or at least it no longer matters if the camera is set properly). The other was the EVF, which in some cases was significantly behind what was happening in reality in front of the camera. Samsung was the first one to solve that problem, by genlocking the EVF to the image sensor. Sony took that further by eliminating the need for mechanical shutter all the time (though this has small side effects, because the all-electronic shutter is a rolling shutter, though a fast one). Now Nikon has taken that one step further with the Z9 viewfinder and removing the mechanical shutter.
The image sensor these days in a mid-range or higher mirrorless camera is typically running at 60 fps as it provides composing, metering, and focus information. The EVF of said cameras also tends to be running at 60Hz (essentially fps). Visual lag is very low now, and typically lower than your response time. High-end mirrorless cameras use some form that's similar to genlocking and can run their EVFs faster, making for very short visual lag. Short enough that I consider it mostly ignorable (I simply learn to adapt to whatever that brief lag is).
One thing that I didn't mention in the above tends to be the same (or at least similar) in DSLRs and mirrorless cameras: shutter release lag. But even here mirrorless cameras have been getting the benefit of all the electronics being stuffed into them: the worst shutter release lag on a Nikon Z camera is better than about half the Nikon DSLR lineup was only five years ago.
The thing about electronic versus mechanical is that we're a long way from what's possible electronically. Moore's law is just now starting to strongly influence the electronics in cameras as we abandon all the mechanical parts and everyone is now using smaller process sizes for their silicon. Yet we're still quite a ways behind where Apple is with their silicon, so there's plenty of room for improvement in the future.
So, the way I look at fast action with mirrorless cameras is this: don't turn on anything that adds delay. With the Nikon Z System cameras in particular, that means avoiding Continuous H (extended), as that changes the EVF response from virtually real time to a clearly lagged slide show of what's already been taken by the camera. There are similar other settings that apply to other mirrorless brands that will change response for the worse. If you avoid those things, I'd say current mirrorless cameras are actually more responsive than the equivalently-priced DSLR now. Thus my simplified answer up at the top of this response.
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It strikes me that many of the answers I'm providing need to be in a sticky article, not in the ephemeral news/views section, where they can be difficult to find after a time. Therefore I'll be adding an article soon in the Cameras section and another in the Lenses section that I'll compile the relevant answers to. This will also give you a fixed thing to link to, should you so desire (links are always appreciated).
