> Blend it with any dry ingredients like sugar before using.

That's the key.

I'm not an expert - and have only experience making/mixing liquids for cocktails - but Gum Arabic (often used to add a thicker mouthfeel in sugar syrups) isn't a great emulsifier but needs to be full homogenised with the oils before adding to more liquid - exceptionally high speed, aggressive blending for longer than it looks like is needed, to create tiny droplets which the gum arabic then stabilises, or the oil will end up separating after a few hours/days.

Sucros Esters, Propylene Glycol, or Polysorbate 80 (which I haven't used) probably do a better job but only Sucros Esters could be considered 'natural'