I recently got approved for a mortgage with a mainstream lender where they took unvested stock into account for the pre-approval. Thankfully I'm not reliant on that stock vesting to pay the mortgage. As I understand there are quite a few lenders that will do this.
“Total compensation” usually refers to base salary together with your yearly bonus and vested stock. Mortgage lenders will typically look at your W2 income which includes the bonus and stock.