Is there some sort of upgrade to Leif's shop? If so, how can I achieve it?
Yes, Leif's shop becomes upgraded as part of the Nooklings' shop upgrades. When you unlock T.I.Y., the two will merge, and from there they share upgrades.
The first level of the upgrade will add two plantable "bush" plants you can buy daily, plus one "furniture" plant like Bonsai and other potted plants.