When using the mesh-type emitter, Object Radius/Object Scale/Particle Size/Particle Radius always output the same value regardless of the emitter’s initial size/size over life settings. In the case of Particle Size/Radius, no value is given at all.
The nodes that you are describing are working as intended. The Particle Size and Radius are only meant to work with Particle Sprites and not Mesh emitters. The Object Radius and Object Scale do not have access to a particle itself, just the emitter object that contains the individual meshes, hence the same value all the time returning.
So is there a way to get the size of the mesh particles from the material editor?
Not from the Material Editor, you could get the value using Blueprints though.
This question popped up on discord and there seems to be a misconception.
ObjectScale material function will give you scale per each mesh particle, as expected.
Just make sure you use it in vertex shader.