This dpeends on the system in use.
For something as simple as the landacape with a single 2km squared tile, 3 or 4 years back, with engine version around 4.22
INTEL wrote a paper showing that changing the texture from 2k to 1k netted a lot more than half the perfoemance increase.
Now, that’s probably unimportant because the landacape system is such a mess that you cant consider benchmarks with it as any kind of standard.
The reality is, its also 4 (or perhaps more) years later, and technology is way different.
The give and take on this is basically RAM cost, which depends on the type of image you have to store.
It also depends on the subserving system that reads in the texture (as they behave differently, regular vs VT).
You have hardware as the unchangable bottleneck and the way you choose to read the texture as the bottleneck you can control.
Obviously, smaller is better.
Less load, less performance drag.
The question you ask yourself should really be: “how small a power of 2 texture can I get away with while this item shades looking like a million bucks”?
If your answer is 4k, then something may be wrong with the model (unless you are rendering cinematics in 8k).
Think about it this way, 4k is the screen size you display at. That is the bigger size to shoot for because people do game in 4k (at 244hz if possible?)
Any objects should be contained within that screensize, so whatever you are depicing should always be smaller than 4k…
Do you really need the object’s texture to be the same size or even bigger than the screen?
(Rethorical as it may be, the answer to that is “it depends”).