This might be a bit of a reach but I've been thinking about this for weeks and trying to find the exact quotations for everything and I finally found what I was looking for. The section I'll be referring to goes:

"Dark side, I search for your dark side
But what if I'm alright, right, right, right here?
And I cut off my nose just to spite my face
Then I hate my reflection for years and years"

There's an ancient Greek play by Euripides called Electra (where we get Electra complex from), and in the first scene Electra is lamenting the death of her father and the exile of her brother and she says:

"my lamentation for my sire, my doleful chant, my dirge of death, for thee, my father in thy grave, which day by day I do rehearse, rending my skin with my nails, and smiting on my shaven head in mourning for thy death. Woe, woe! Rend the cheek;"

It's nuanced and hard to explain without going on for pages, but Electra's trauma leaves her with her love for her father and brother, both of whom she lost as a young child, as the closest thing to romantic love that she has. What this quote refers to specifically is the practice where women in mourning for a husband or father would disfigure their own face and pull out or sheer their hair. This symbolizes a sort of commitment to the late loved one, basically saying I don't want anyone to be attracted to me or love me romantically ever again now that I've lost you.

To be clear, it’s definitely a reach to assume that this is what Taylor had in mind when she said "I cut off my nose just to spite my face," but this reading is really interesting to me looking at this song through a queer lens. She says "what if I'm alright, right, right, right here?" which makes me think of Right Where You Left Me. To me she is weighing the options of, do I come out and enter the combat (homophobia) or do I stay here and mourn the loss of my lover by spiting my face. As if to say, you made me feel beautiful and now that I can't have you, I don't want to feel beautiful ever again.