There is a mathematical relationship between the sensor size and the optical properties (particularly focal length) of the lens that affects the result.
Bigger sensors tend to have shallower depth of field for a given aperture, which requires stopping down the lens further or using lens movements to compensate to keep the subject in focus. But that can be desirable where you want to isolate a subject or otherwise create an effect.
However, stopping down further also tends to cause an increase in diffraction as the Airy discs become larger and start to engage each other in constructive/destructive wave interference which reduces the theoretical resolution of the system. This particularly affects smaller sensors but since you stop a larger lens down farther it also affects them as well.
And in contrast - smaller sensors need wider apertures for a given amount of subject isolation, but they are also subject to diffraction at much wider apertures. This means you need a lens that can deliver maximum resolution at very wide apertures. This is why your cellphone camera has a f/2 or f/1.8 lens, the sensor is tiny and it needs a very wide aperture or diffraction will rob the image of all sharpness. It's also why, for the most part, cellphone cameras haven't gone much above the 10-12mp range.
(I've always suspected there is probably some asymptotic limit to the amount of resolution that can be extracted for a given amount of depth of field, even with an infinitely large film/sensor size. as you increase the sensor size you have to stop down further and the diffraction becomes stronger and limits the lp/mm)
Yes for me when making large prints. You don't get good prints at less than 150 dpi enlarged, generally, and 300+ dpi is preferable and more comparable to a large format negative, so you'd like a ~75 megapixel camera just for poster sized prints, and more for prints larger than that.
Note some people use large format negatives for ultra-sharp small prints, in that case you might be looking for 1000 dpi or higher to match the fidelity of a large negative.
Diffraction and airy disks have an impact as mentioned by a sibling comment, but the simplest explanation I've used is that ultimately you're capturing photons, and if you have a larger sensor you can capture more photons. More photons are better. Of course you need a larger lens with a longer focal length to match the same field of view, but that's the basic idea.
