The odd thing about steam engine nomencalture is that the steam part is the transmission - really they would be coal-steam ( like diesel-electric ) or whatever. That sounds a bit daft though... although it does leave room for things like electric-steam, as the swiss once did.
AFAIK no one ever built a purpose made electric steam locomotive, in which electricity is used to boil water.
The Swiss did I believe modify a few old steam locomotives by fitting banks of electric heating elements. It is not clear as whether the heating elements were placed in the fire box or in the water space of the boiler.
This was said to be only a very short term measure, pending the delayed delivery of "proper" electric traction.
The efficiency would be very low, but was worthwhile in the special case of the electricity being virtualy free after sinking capital in building hydro electric plant.
Better to use virtualy free electricity inefficiently than to buy imported coal or oil fuel.
I think that some Scandanavian electric locomotives had low pressure electric steam boilers for cariage heating, prior to to the introduction of electric heated stock.