There's no clear answer on this - some count it as a spending line-item, others count it as a saving line-item at different levels in the investment order. All depends how your rent vs buy market is in your particular location, and how much you value home ownership generally.
For myself, I'm diverting what would have been post-tax savings in a brokerage account into my downpayment fund, after maxing my 401k and IRA. So, between steps #5 and #6 (though you could also call it between #7 and #8, since neither 6 or 7 applies to me). We have no debts, our emergency fund is adequate, and our HSA is maxed through my husband's paycheck.
However, for someone who doesn't make enough to fill all the tax-advantaged space, I think it would be fair to move down payment savings up a few rungs. All depends on your own specific situation and values.