For a given thickness, the optimum airfoil shape will not be a plate with constant thickness (i.e. a flat plate), at least in terms of lift and drag.
I agree, but in case of an extremely low Re along with a rather thin flat plate wing, the air molecules "reshape" the plate into a cambered airfoil (at a positive AOA).
As the Re gets smaller, the required thickness gets smaller, but there are also drawbacks for being too thin e.g., the max thickness point has to move forward and its distribution along the airfoil becomes critical as well.
If you want an airfoil for an extremely low Re that also has a wide speed range, the job gets rather tricky.
I think designing really good airfoils for extremely low Re is one of the most difficult challenges in the model aerodynamics.