Sorry, somehow I missed your post. In addition to what you said (relationship, spiritual) I do think it also referred to physical death. However, in his mercy God delayed that, and instead killed animals to clothe them with skins. This was essentially the first symbolic animal sacrifice, ultimately pointing to Christ's sacrificial atonement on the cross when He - the woman's offspring - would crush the serpent's head!
JMHO. DYODD. Watch List: FRHC, AVCO, TEUM, SURG, DMGGF, IMTL