Resolution is the ability to separate two parallel lines next to each other or separate two dots next to each other. That's why when you read the charts for the resolution of a lens it's given as line pairs per mm (LP/mm) or line widths per picture height (LW/PH) or for printers dots per inch (dpi). It is a linear measurement - measurements along a line in units of length. Area depends on length squared, measured in square mm or square inches etc. The total number of pixels is measured by the number of pixels in an area, not along a line of distance. When you double the number of pixels in a sensor, say from 22 Mpx to 44 Mpx, you don't double the resolution, you increase it by the square root of 2, ie by 41%. To double the resolution, you would have to increase the number of pixels in the sensor 4x to 84 Mpx. The same is true if you double the number of pixels in an image by doubling the focal length of a lens - although you increase the number of pixels by 4x, the distance between two parallel lines or two adjacent points is increased by only a factor of 2, the square root of the number of pixels. So, resolution varies as the square root of the number in an image.
That's now two beers or glasses of peaty malt whisky you owe me. It will soon be worth my while driving to Alsace to claim them.
