Yes! There are applications of “Topology 101” that are not Euclidean spaces, e.g. “Totally disconnected” spaces show up early on in number theory, and the Zaris

Yes! There are applications of “Topology 101” that are not Euclidean spaces, e.g. “Totally disconnected” spaces show up early on in number theory, and the Zariski topology associated to an algebraic variety/scheme is foundational in algebraic geometry. That said, any mathematician calling themselves a “topologist” is likely studying things like homology/homotopy or generalizations which mostly apply to Euclideanish spaces.