Some of the Physics.
Newton's Second Law of:
Force = Mass x acceleration
a
pplies as soon a 'firing' commences.
For a propulsion system the thrust must be caused by the force of the propellant against the rocket. This will, indeed, invoke Newton's Third Law, so the rocket will move in the opposite direction.
The coke bottle ejects water according to F=ma, but the problem is one of inertia as well as thrust. That bottle is heavy at maximum force (Force = Pressure x Area) and acceleration will be reduced, but as the bottle gets lighter (reduced water content) the force will reduce because the pressure is dropping (not like a space rocket with diminishing mass, but constant force).
It is a balance of pressure and volume of water expelled for our coke bottle and there will be an optimum fill volume for any given pressure. Too little water and the thust will disappear before the rocket has achieved maximum velocity and too much will mean the pressure will be much reduced, thereby expelling water more slowly while still with a high inertia. Added to that, the water being expelled at low pressure will have little increase in velocity in the opposite direction of rocket direction. Of course, the aperture area through which the water is being expelled will have an effect also (ignoring the ever present air friction as the rocket moves faster).
Nothing simple, but while momentum must be conserved, the momentum of the water contained in the bottle and ejected from it will be a very complicated system, with forces of gravity dragging the whole lot towards the centre of the Earth whether inside or outside the bottle! Momentum is easier to sort out when a couple of bodies strike or become a single item.