I understand the thought and technicalities of your primary residence being a liability (even though I disagree with it!) If it doesn't bring you a return or bring money in, it's a liability.
However, you have to live somewhere. Would you also not call renting a liability, even though there's no mortgage, there is a lease. Unless you live in a van down by the river, you're going to pay to live somewhere.
Since it's a househack and you're bringing in income (even if the tenant isn't paying 100% for your expenses), I'd call it an asset. Without it, you wouldn't be bringing in that additional income, and you'd likely be paying out more per month in your budget (for rent elsewhere).
I think folks try to make this black and white, but that's the beauty of real estate investing. Nothing is black and white, right or wrong. Just what you decide to do with it.
Regardless of asset vs liability, it's still a great way. to build wealth ;)