How do I report the purchase of a second home that my estranged wife bought and moved in to?
You do not report the "purchase" of the home.
Go to Federal> Deductions and Credits> Your Home to enter mortgage interest, property taxes, private mortgage insurance (PMI) and loan origination fees (“points”) that you paid in 2020. You should have a 1098 from your mortgage lender that shows this information. Lenders send these in January/early February.