My first thought was that expanding foam from the hardware store is very cheap, but obviously that sort of foam would be crushed by the water pressure.

> Syntactic foams are composite materials synthesized by filling a metal, polymer,[1] cementitious or ceramic matrix with hollow spheres called microballoons[2] or cenospheres or non-hollow spheres (e.g. perlite) as aggregates.[3] In this context, "syntactic" means "put together." [...] The compressive properties of syntactic foams, in most cases, strongly depend on the properties of microballoons.

I wonder how similar its properties are to air-entrained concrete.

Not very because air-entrained concrete has very little resistance to crumbling and doesn't handle tensile stress well (which you could fix by adding fibers or some other element that handles tension better, hence reinforced concrete). It has plenty of applications under normal atmospheric conditions but for submersibles you will want something with entirely different properties.

clowns. the pressure hull of a deep-sea submersible is not the place to go looking for cost savings, especially when the target clientele is cost-insensitive billionaires.