Hi there, welcome to the forum and thanks for your observations from using your Sony A7R3, a new camera to this debate on here I think and one I’ve considered buying myself.
Your observations seem to fit in with the science, if the sensor is moved in discreet steps equal to the pixel pitch it can’t in theory increase the resolution, only the colour information as your 4-shot experiment has shown. This essentially ensures that each pixel site (red, blue and 2 greens) on a Bayer sensor actually measures the density of light rather than interpreting it from its neighbours. In order to increase the resolution it needs also to move in increments equal to half the pixel pitch so you get 16 or 32 shot modes.
The pixel pitch of your camera is 4.5 µm or 4.5 thousandths of a millimetre so for the science to meet reality the camera has to be very solidly mounted and stable during the exposure.
What has made you see that the colour has improved dramatically, is there anything that you can share?