Does every omega-categorical structure admit a continuous realization of all its types over finite sets, and if not, which dividing lines in classification theory exactly characterize when this fails?

The problem asks for a complete structural characterization of which omega-categorical theories allow types over finite parameter sets to be realized in a topologically continuous and definably uniform way as the parameter set varies. The recent counterexample to Kanalas' problem shows that continuous realization of types can fail even in seemingly tame omega-categorical structures, but it leaves open whether there is a meaningful classification-theoretic boundary, such as stability, NIP, or some finer combinatorial tameness condition, that precisely separates the theories where continuous realization always works from those where it breaks down.