What can we say about continuity by knowing Borel-Measurability?

Question

I've seen in multiple posts (e.g. here, here and here) on how continuity properties of functions imply Borel-Measurability, in a very natural way relating the topological definition of continuity with the definition of Borel-Measurability itself. I'm wondering if everyone knows about results in the opposite direction: what can we say about continuity properties (e.g. continuous, almost surely continuous, countably-discontinuous, or even other definitions of continuity such as equicontinuity, and so on) by knowing that a function is Borel Measurable?