I would say that the key thing is to construct the right interactions between electrons. That said, the geometry (or structure, as we would generally say in condensed matter physics) is one of the key parts of what determines the interactions in a material, so this is certainly one approach. In practice, it is difficult to tune the structure of most materials except by applying pressure, or by changing to a different (possibly related) material, so finely tuning the interactions by influincing the structure can be difficult (twisted bilayer graphene being a notable exception).
> Regardless of the underlying quantum mechanics, there's a large opening for experimental physics here. Are there edge effects, what about grain boundaries, etc.
I agree! Topological insulators and their surface states (which are in some sense "edge effects") is a pretty hot topic right now. Related to superconductivity, the research group I'm working in has been playing with introducing disorder to unconventional superconductors by plastically deforming them (i.e. squeezing them until we start to mess up the structure). Surprisingly, this has actually increased the superconducting transition temperature in some cases [0][1] (full disclosure: I'm one of the authors of this paper). As far as we can tell this "strain engineering" of the electronic properties of superconductors is basically a new subfield, so there's still a lot to learn. One of the difficulties is that in unconventional superconductors (which includes the high-Tc superconductors), theorists tend to prefer to work on idealized models of materials, since the calculations are difficult enough without introducing disorder, defects, etc. in addition.
[0] https://www.nature.com/articles/s41563-021-01102-3 [1] https://arxiv.org/abs/2005.00514 (same paper as above, but in a non-peer-reviewed and paywall-free version)