Effect of motion on ball in a moving cart

I think your terminology is confusing you - the correct term is pseudo-force, not pseudo-acceleration.

Introducing a horizontal pseudo-force in the reference frame of an accelerating cart allows us to pretend that objects that are stationary in the reference frame of the cart are in equilibrium, even though we know they are really not.

If the cart is moving with constant velocity (i.e. zero acceleration) then objects that are stationary in the cart’s reference frame really are truly in equilibrium, so we do not need to introduce a pseudo-force.

Another way to look at this is to note that the pseudo-force on an object of mass $m$ will be $ma$ where $a$ is the cart’s acceleration. But if $a$ is zero then the pseudo-force is also zero.