What is the minimum distance from the floor for a 1/2 bath power outlet?
A receptacle not serving the basin has no height requirement in a dwelling unit, but...
2017 NEC 210.52(D)Bathrooms. At least one receptacle shall be installed in bathrooms within 3 ft of the outside edge of each basin...In no case ...be located more than 12 in. below the top of the basin.
I don't have record of when this was adopted but it isn't highlighted grey in the codebook, so it has been in there since 2014 at least.
I think it may have been possible if the switches are within 3' that there was a receptacle and switch, the switch fed both the light and fan but somebody removed the receptacle to have space to put a timer on the fan. If it is only one circuit in that switchbox and it feeds receptacles outside of this bathroom it wouldn't meet current code. I don't know what the code said when built but modifications are required to meet current code.