Should I add my current supervisor as the coauthor of my paper if I am going to transfer to a new university?
Everyone who makes a sufficient contribution to your paper for authorship should be an author on your paper (and no one else).

It doesn't matter what institution they are at nor does anything else: everyone that contributes at a level appropriate for authorship is an author.

Standards for what contribution constitutes a sufficient contribution for authorship vary by field, and your plan to consult both your new and old advisor is a good one because part of their mentorship is in helping you make decisions about what governs authorship in your field.