The hide option hides edges you select before pressing H. It doesn’t hide your whole mesh. Not quite sure how you can “display invisible edges”. Doesn’t that make them visible again?
In F9, MeshTools 1, you can turn on ‘All Edges’ (for object mode) but you can’t decide which edges it will and will not draw when it’s off.
Same place you can turn on ‘Draw Edges’ (for edit mode) that will draw edges in edit color (but all edges are drawn in black in edit mode anyway).
You can also click “Faster” and “Slower” to increase/decrease the number of edges displayed on a mesh. Not sure if this has anything to do with what you want but it might.