I am unable to find the size reference while changing background image of the Welcome Banner plugin. Is it 1600×400 px?
Do you mean this theme component? Welcome Link Banner… the background image for that should be at least 1110 x 216px, but it will scale to fit the available space.
Or If you mean the built-in welcome banner feature, found at /admin/config/welcome-banner — then this image should be at least 1089 x 177px, this image also scales to fit the available area using background-size: cover
Scales the image (while preserving its ratio) to the smallest possible size to fill the container (that is: both its height and width completely cover the container), leaving no empty space. If the proportions of the background differ from the element, the image is cropped either vertically or horizontally.