As someone who's monkeyed around with several other-model shock swaps on an older little Ninja, and now owns a 400, I can provide some input.
The 400 uses an eye for the bottom shock mount, rather than a clevis. It will not directly bolt onto a 250/300/500.
https://www.kawasaki.com/Parts/Parts.../2018/EX400HJF You may (or may not, I don't know) be able to also swap the suspension knuckle from the 400 to make it mount up. Keep in mind that if its dimensions are any different from the original knuckle, you're altering how the suspension operates. That could be better, worse, or the same in the end, but you're changing another aspect of the suspension actuation, and you need to consider that.
Other than the mounting differences, the 400 shock looks pretty similar to the NewGen/300 shock. It appears to be a standard minimally-adjustable, non-rebuildable budget shock. According to
RT's data, it's a 575lb/in spring. The EX500 is 300lb, the PreGen is 440lb and the NewGen is 520lb. It's my understanding that the 300 shock is the same as the NewGen, but possibly with slightly different valving. Unless a 575lb spring happens to be perfect for you, I see no reason to use the 400's shock, especially considering the other work you'd need to do to make it fit.
The second gen SV650 shock is a similar budget shock with only preload adjustment, and a spring about the same as the PreGen's. It requires similar mods as the GSXR shock to fit, but the cheaper clevis is easier to deal with. If I were looking for that spring rate (
RT says that's pretty close for your weight), I'd personally get an EX500 shock (threaded preload adjuster but super-soft spring) and swap on a PreGen spring (no preload adjustment at all but a good spring for your weight), since it's a drop-in replacement requiring no mods.
https://www.invisibill.net/ninja/EX2...50F-length.jpg
A GSXR shock is more adjustable, rebuildable, and available with a variety of spring rates (and apparently mounting styles with the newer models). If you're looking for a real "shock upgrade" from a budget swap, this is really the only way to go. If you're looking for a dirt-cheap, acceptable "respring" to match your weight better, one of the other OEM shocks may suffice. Technically a swapped shock from another bike won't have as good a match between its valving and your bike/spring, compared to going out and buying an aftermarket shock/spring specifically for your bike/weight, but it's WAAAAAAY cheaper and can still be a huge improvement over stock.
As for fork springs, I would suggest getting the proper spring rate eventually, but the NewGen isn't too horrible stock. You're looking at about 15% stiffer springs. For comparison, the EX500's fork springs are very soft, and I'm a bigger guy, so RT's calc says I would need 69% stiffer springs under the same conditions. It's less than ideal for you, but it's not the gross mismatch I had in stock form.
If you're considering RT Emulators, I suggest checking out
Ricor Intiminators too. They're a similar drop-in fix for the basic damper rods, but they use shims similar to cartridges rather than the same fixed-orifice damping as the stock rods. Whereas Emulators have a spring-operated blow-off valve for releasing "overflow" pressure beyond the standard fixed orifices, the Intiminators have an inertia valve that opens from the wheel bumping up. This should mean that you can apply as much downward cornering pressure to the suspension and it will act based on just the shim damping. When you hit a bump, the overflow valve kicks in and allows the wheel to "ignore" the shim damping and quickly react. I have no personal track experience, but this seems like something that's actually more suited to the street (I assume tracks generally have fewer bumps and potholes than the street, though I realize they're not perfect surfaces either.)
The Intiminators are tweakable with different shims. This could provide a poor man's version of a cartridge upgrade. They work quite well as a drop-in, and they're newer than Emulators, so there aren't many people who have a lot of experience with tinkering on them. I think they have more potential than Emulators, but you may end up having to figure things out on your own with trial and error. With Emulators, you probably have a better chance of finding someone who can set them up perfectly, even if they aren't theoretically quite as good as Intiminators. 90% of 100 and 100% of 90 both work out to the same value in the end (and 50% of 100 works out to way less, if you do a bad job setting up the best product).
As another bonus, Ricor says the Intiminators actually work better with slightly less spring, compared to Emulators. If you go that route, the stock fork springs may be even less of an issue right now.
FYI, actual 250 racers here have posted that their real-world suspension numbers don't match what RT's calculator suggests. I don't personally have any better suggestions, but just be aware that their numbers aren't necessarily the be-all, end-all of the discussion.