As I said in another thread, Shar being someone calling themselves the Absolute fits her lore. I vaguely even remember in one of the old FR novels Shar referring to herself as "Absolute" or at least as something akin to being "absolute."
I agree the "avatar" reference is probably just terminology for the PC. However, it is possible the PC is a Chosen of some god. Chosens emerged as a prominent theme only in 3e lore and thereafter (so after the original BG games), and a Chosen can be an ordinary person to whom at some point a god gives a part of their divine essence. So the PC may be already selected to be some god's Chosen, but who has not yet received the god's essence (or the essence is currently dormant and the PC doesn't yet realize they have it in them).
