So according to this Issue on GitHub. It seems to be normal behaviour.
They basically said, that you cant use plane mesh with plane collider in combination with KinematicBodys.
So your solution would be to use something other than planes. Read the issue for more information.
I recreated a simple scene similar to yours and can confirm that.
Here is my Player script for a
KinematicBody, if you need a comparison.
export var speed = 10
var velocity = Vector3(0,0,0)
velocity = move_and_slide(velocity)
var direction = Vector3(0,0,0)
direction.y -= 1
direction.y += 1
direction.x -= 1
direction.x += 1
var motion = direction.normalized() * speed
velocity.x = lerp(velocity.x, motion.x, 0.2)
velocity.y = lerp(velocity.y, motion.y, 0.2)