Is Krishna supposed to be a symbolic deity, or an actual physical incarnation?

In a way you are right when you say Krishna IS BrahmaN. But if you go deeper in to Maha Vaakyas like "Tattvamasi" & "Soham" you will realize that all is BrahmaN. Where "Tattvamasi" ( That 'BrahmaN' is You) is Paroksh Anubhuti, realization of oneness with BrahmaN through the experience of other person. "Soham" (That 'BrahmaN' is I) is Aparoksh Anubhuti, realization of oneness with BrahmaN by self. Person with such realization becomes BrahMchari in true sense. Shri Krishna as an Avatara had been completely a self realized person so is known as Purna Purushottam and BrahmaN himself.But many of the other deities reflect some particular aspect of BrahmaN not complete Brahmn so they don't fall in the category of BrahmaN himself.