If you calculate the area of a rectangle, you just multiply the height and the width and get back the unit squared.
Example:
5cm * 10cm = 50cm²

In contrast, if you calculate the size of an image, you also multiply the height and the width, but you get back the unit - Pixel - just as it was the unit of the height and width before multiplying.
Example:
What you actually calculate is the following:
3840 Pixel * 2160 Pixel = 8294400 Pixel

What I would expect is:
3840 Pixel * 2160 Pixel = 8294400 Pixel²

Why is that the unit at multiplying Pixels is not being squared?

Because "pixel" isn't a unit of measurement: it's an object. So, just like a wall that's 30 bricks wide by 10 bricks tall contains 300 bricks (not bricks-squared), an image that's 30 pixels wide by 10 pixels tall contains 300 pixels (not pixels-squared).