Our garden shed has a fine mist of tiny black droppings across the floor -
and also across some of the toys/garden furniture.

They are truly miniscule - 1mm at the most - more like black dust.

From reading up on droppings of household pests, I've ruled out any rodents
(they are far too small) so I'm wondering what's creating them? Some kind of
insect or spider?

I'd appreciate any/all help in identifying these!