True.
If you take a linear-rate coil spring and cut in it half, you will end up with two coil springs of a higher linear-rate, meaning it will take more force to compress the cut coil per inch than it would to compress the original coil
A steak is not a coil spring.
Everything that can compress is a spring. A piece of foam is a spring, an eraser is a spring, metal is a spring, as long as they don't went too far into the plastic region and stay inside the elastic region, it will go back to the same position after you release your force / weight, it is a spring.
Go get a scrap spring from a mechanical pencil, and cut it in half. They don't become stiffer and take more force to compress per inch. The number of coil per distance travel hasn't change.
So back to your equation:
Where k=spring rate; d=diameter of the spring wire; G=shear modulus of elasticity of the spring material (11,500,000 for a steel spring); D=mean diameter of the spring's coils; and N=number of active coils.
k=(Gd⁴)/(8ND³)
Your material hasn't change, so G hasn't change. Diameter of your wire hasn't change, so d hasn't change. Diameter of your spring coil hasn't change, so D hasn't change.
In order for your understanding to be correct after you cut the spring you have to PULL IT LONGER back to the original length as well. That way the spring slope sharper, and would be stiffer. But if you didn't pull it longer it would still be the same N.
The N here is number of active coil for the total spring length (total spring length is not in this equation). If you reduce both the number of coil AND the total spring length at the same time, this equation doesn't apply any more. The k here also has the force per total spring length in unit. They cancel each other out. So if you are not keeping the total spring travel length the same as before, by cutting the spring, this won't be stiffer.
The equation should be k (spring rate) = F (force applied) / L (total spring length) = (Gd⁴)/(8ND³) = (Gd⁴)/(8(n / L)D³)
where n = number of total coil turn, L = total length of the spring and N is really number of coil turn / total length of the spring that your link didn't mention.
So if you cut the spring you are having the same number of coil turn per spring length and N doesn't change because you are not changing the slope of the spring (which is what number of coil for the same length really is).
https://engineerfix.com/what-is-spring-rate-and-why-does-it-matter/
So, your total spring "rate" is the same because your distance and number of coil both reduce. However, because your total spring length is reduced, the total force it can support for the same rate is reduced.
Thus, you have a weaker total spring for the same car weight and it will bottom out sooner.