Seems people were even trying to use the expansion of "liquefied air", sort of like a steam engine.
Yes, it's all expanding gases. (TDC=Top Dead Center, ICE=Internal Combustion Engine)
The standard ICE, needs to get rid of excess heat, only after it's been used to push the piston. (up though TDC)
The steam engine (formally speaking, it's really just a motor) needs to retain heat until it exits the cylinders(or just before, starting at TDC).
The air engine(also just a motor), needs to acquire as much heat as possible just after the intake valve(or whatever it has) closes, up though TDC.
Which is a very different proposition from the first two.
Difference between an engine and a motor? The engine generates the pressure (or pressure head) inside, as part of the process.
Motors only convert potential energy into kinetic. So that includes electric motors.
If your compressed air is in the form of liquid-air, it needs to be preheated in a high-pressure trap until used. And then it still benefits from more heat input. In fact, an interesting combination would be using the waist heat from an ICE to heat the cylinders of the air motor(only if using compress air supply). A hybrid of sorts.
The reason you would not use waist heat to expand ambient air, is that energy used in moving the extra weight of that hardware often exceeds the power generated. That is, using a hybrid of ICE and Stirling (or an Ericsson) together, these heat motors are more useful when not in a moving vehicle, and near to an available heat source, that is otherwise being wasted. (called a bottoming cycle, or post-cycle)
And then there is the cost, does all this extra cost of equipment off-set the value of energy saved? Generally not in a moving vehicle.