If it were me-
1. Notify my insurance company
2. Buy immediately everything needed for balance of trip.
3. Make a list with replacement cost of all missing items.
4. Send documentation for #2 & #3 to both the hotel and insurance company.

Whatever the hotel pays (whether from the hotel or their insurance) reduces your loss and balance is from your insurance.
I would hope the hotel makes you whole and provides some type of additional compensation (whether cash, free nights, points, etc.)