Is there such a thing as a "minimal soap" molecule?
It boils down to the definition of soap. Wikipedia defines a soap as the salt of a fatty acid.
IUPAC claims the smallest fatty acid can be considered to have 4 carbons.
Therefore the simplest soap molecule would be a (generally sodium) salt of butyric (butanoic) acid, i.e. sodium butyrate.

Now apart from the chemical definition, a soap must adhere to its function in order to be defined as such. Therefore, before calling something a soap, we would have to know if the substance does in fact act as a surfactant in a oil-water surface (reducing the interfacial tension) - but that will depend on the nature of the oil in question and the purity of the water. Only for a well defined system we can then conclude that such molecular salt is acting as a soap in it.