The bottle cap generally is polypropylene. It's properties are needed to maintain the seal. The bottle is polyethyleneterephthalate (PET). It's properties are needed to keep the gas inside, among other things.
It's easy to recycle either if they are separated. PET can be recycled easily, or turned back into the component monomers easily, and chemically, this is all well known operations. You don't need some fancy enzyme, but you do need source separation.
Most "plastic" by far is polyethlyene (PE) which also can be recycled, easily, if you get a nearly pure stream.
The white packaging foam is polystyrene, which can be converted back into styrene and reused, easily, IFF it is separated into a pure stream.
The issue with all of these fancy sounding techniques is source separation, not chemistry.
