At least this amount will, assuming it’s just taxes and insurance, be due every month for as long as it’s owned. Property taxes in California for example are around 1%/year (so a $377k home would be around $4k/year).
If you own the home outright you may not need insurance, but of course, that’s a risk.
Taxes may be severely limited in how much they increase (see: California prop 13), so while they will likely increase it may not match e.g. rental increases.