Do smaller organisms (eyes) see smaller objects in greater clarity?

There are several independent limiting factors.

I will discuss several of those, starting at the retina.

The retina is the layer of light sensitive cells at the back of the eye. If those cells are relatively large they don't need much light to be triggered by incoming light. A retina consisting of large cells is good voor being able to see in low light conditions, but not good voor sharpness of vision.

In the real world small creatures generally go out in the open rarely, as they are vulnerable there. Small creaturs tend to remain under cover, meaning that they live their lives predominantly in low light conditions.

Another limiting factor is precision of the lens. A lens that is manufactured with technology can be ground to a high level of precision, such that it is capable of casting a very sharp image.

Biological lenses are pretty good, but it seems likely to me that there is an upper limit to how good they can be.

A more technical limiting factor is called 'diffraction limit'. It's too technical to discuss in this answer, but the takeaway is that the edges of the aperture introduce distortion (due to diffraction), so that it is advantageous to have a lot of area of light gathering, and comparitively little perimeter. A smaller diameter of the aperture means that the imaging is more diffraction limited.

Lastly, back to biology. Predatory birds that hunt in daylight have a reputation of having the sharpest eyesight in the animal kingdom. They have to recognize prey all the way down on the ground, and they can afford to have poor low light vision. It seems likely that in the case of predatory birds the process of darwinian evolution has resulted in predatory birds having the smallest light sensitive cells in their retina.

I acknowledge that this doesn't actually answer your question. Predatory birds are good at seeing sharp a distance. It may well be that their eyes are not equipped to accomodate to seeing close by. It's a trade-off. It is quite difficult to have such a range of accomodation that you can see sharp both in the distance and nearby.