Nikon D5600: AF area mode (no of focus points ) doesn’t work in any of manual mode (aperture, shutter, manual) for any focus Mode?

The dynamic focus modes require you to be in AF-A or AF-C.

The dynamic modes (d9-d39) only show the selected focus point as active. By default the selected/active point is the center point, but you can move it manually. The camera then uses other focus points as needed/allowed, but it doesn't show the focus point moving. The focus point that was actually used will be reported in the exif/focus point review.The camera will highlight all of the enabled focus points in the viewfinder when the setting is being selected/changed.

If 3D is active it will/should show the used focus point moving in the viewfinder; but by default it also starts with the center focus point by default.

Auto is the only mode where the camera is using multiple focus points simultaneously and shows that in the viewfinder... but still, only one point (distance) can ever actually be at maximum focus.