I am trying to incorporate a TEC in a portable system. The heat from the interior of the system needs to be transfered to the exterior where it can be dissipated freely into the environment. Now, I have developed a thermal management design where heat is conducted outside via sheets of copper and will be ultimately deposited into a fabricated "water heatsink" where temperature differential is mitigated by water's high specific heat capacity and additional surface area. The water heatsink is consisted of coppersheets forming a thin container filled with water. The system needs to be compact and lightweight and this system seems to provide heat mitigation capabilities and an increased surface area.
Water has some great properties for cooling, but it's messy, and awkward to control. So if you're going to incorporate it, make it work.
In your present diagram, its high heat capacity means it can absorb a pulse of heat better than a metal heatsink.
However, water is a poor conductor of heat, so it's actually insulating the bottom of the heatsink from the top, it's worse than just having a metal heatsink there, if the heat is going to be generated for any length of time. Heat is flowing top to bottom, so natural gravity driven convection is not going to occur
What it does do well is convection cooling, as it has high heat capacity and low viscosity. If you're going to the bother of using water, then pump it, to flow from a small hot emitter under the TEC hot side, to a large heatsink elsewhere.
A large, finned, radiator, cooled by either natural air convection, or a fan.
A large mass of water, large enough that it doesn't heat up sensibly in your operation time (a bucket, a stream).
An evaporative (bong) cooler (fan assisted evaporation of the cooling water).
If you can't flow water to one of these heatsinks, then I wouldn't bother trying to incorporate it into what looks like a basic conduction-path metal heatsink.