You are correct. It has nothing to do with "magnification" of smaller photosites. There are two major differences. The first is in noise. A smaller photosite captures less photons, so the signal has to be amplified more. Because signal to noise ratio is lower, it brings the noise floor up for the same amount of signal. This is most visible at higher ISOs. The second factor is a bit more esoteric, and it has to do with the physics of optics. To have the same angle of view projected onto a smaller sensor, you need a shorter focal length lens. A shorter FL lens has more depth of field than a longer FL lens. This means that at the same aperture, more will be in focus on the smaller sensor. This can be an advantage or a disadvantage, depending on your preferences and needs. If you want a shallow depth of field in order to isolate a subject from the background, for instance, you are better off with a larger sensor. However if you want more in focus, then the shorter FL on the smaller sensor is preferable.

There is another point to consider about noise: A slower lens on a larger sensor will give you the same amount of noise in the final image as a faster lens on a smaller sensor, so having, say, an f1.2 lens on a MFT sensor might sound impressive, but the results (in terms of noise), are roughly equivalent to using a f2 lens on a FF sensor. That being said, it is clear that for equivalent performance (in terms of noise), you can have smaller lenses and a smaller body using a smaller sensor. The only real questions are about low light performance and depth of field. In terms of sharpness, pure and simple, it depends on lens design, but a well designed lens for MFT will resolve as much or nearly so as a well designed lens for FF of equivalent angle of view. Just look at the resolution of phone cameras with their tiny sensors, and you can see that "magnification" of pixels has nothing to do with anything.

Since you're talking about hypothetical so let make an example on hypothetical situation.

One camera with the sensor of 24x36mm using a 45mm lens set at f/8.
The other with the sensor of 16x24mm using 30mm lens set at f/8.
Both sensors have 24MP which is 4000x6000 pixels.
Both used to take the image of the same scene from the same location and the lighting doesn't change.

1. The image from the camera with the smaller sensor is likely to have more noise but that isn't a given because if it's better made it can have the same or even less noise.
2. The image from the smaller sensor has more depth of field.

I ask this as a hypothetical because I don't want to get into debates about camera brands or models. Suppose I have two raw files, both 24 megapixels, both with the same subject filling the frame, both with "Normal" lenses, shot with identical exposure. All other conditions identical.

What differences in image quality would I expect between these two files based only on the difference in sensor size? What about enlargement, would there be differences in quality of an enlargement based only on the sensor size difference?

I've read that in enlargement the larger sensor would be better because it would not have to be enlarged as many times as the smaller sensor due to the larger original area, but this doesn't make sense to me if the smaller file has crammed in the same number of megapixels and the full image fills the frame and covers the subject with the same number of pixels. I thought pixels were dimensionless once they were in a raw file.

I ask this as a hypothetical because I don't want to get into debates about camera brands or models. Suppose I have two raw files, both 24 megapixels, both with the same subject filling the frame, both with "Normal" lenses, shot with identical exposure. All other conditions identical.

What differences in image quality would I expect between these two files based only on the difference in sensor size? What about enlargement, would there be differences in quality of an enlargement based only on the sensor size difference?

I've read that in enlargement the larger sensor would be better because it would not have to be enlarged as many times as the smaller sensor due to the larger original area, but this doesn't make sense to me if the smaller file has crammed in the same number of megapixels and the full image fills the frame and covers the subject with the same number of pixels. I thought pixels were dimensionless once they were in a raw file.

That's the wrong word (normal) that just exasperates a general misunderstanding between 'equivalent field of view' with 'equivalent focal length'. The question / assumption is further exasperated by 1.5 vs 1.6 crop factors for different brands of cropped sensors. The prior linked example attempted to find two Nikon primes that come out to the same equivalent field of view while maintaining the same f/1.4 maximum aperture.

If we remove the 'how' / 'what lens' technical aspects of the question, the visual differences are in the out of focus areas, if any. One would expect some noise differences, more pronounce the higher you get away from base ISO for the two cameras.

When you consider the sizes of the sensors, this idea of magnification to get to the same print size should (could) magnify the noise in the image from the cropped-sensor by a larger factor to get to the same print-size. This issue is going to be more noticeable at higher ISO values, in theory, but this generalization would have to be demonstrated by specific / actual 2019 comparisons of equipment to confirm.

I prefer published examples rather than generalized expectations, such as this additional example of the same question: https://petapixel.com/2017/10/03/full-frame-vs-crop-sensor-shootout-can-tell-difference/

Wow, that was interesting though I did get all of them correct! I am surprised they look so similar and I don't own a FF digital camera only five APS-C cameras. But I have decades of experience with 35mm film cameras and apparently a good theoretical understanding of the issue at hand. To do the experiment myself approximately I would need a FF Pentax K-1 or K-1mkii (36MP) matched to my CF Pentax K-3 (24MP). I could actually try a couple different experiments as I have several similar 50mm lenses and well as 35mm lenses. But personally, if I could I would prefer a Full Frame over a Crop Factor.

A uncontrolled example I have there is my 24MP Pentax K-3 (1.54 Crop Factor) in low light produces a horrible image, and a friend's 24MP Nikon D-750 FX (Full Frame) produced nice images at the same indoor event. Though I probably should actually try a more controlled experiment comparing my K-3 (24MP) with my K-5 (16MP) that is said to be a low noise camera.