You have a good point, and I appreciate the evenhanded approach. I'm still far from sold that "poverty wage" is a useful term if we want to have a healthy discussion. It leaves too much nuance out.

It doesn’t though. Poverty is well defined (and is defined based on the number of people in the household).

https://aspe.hhs.gov/poverty-guidelines

So wages should be linked to the number of people in the household? Workers with more kids should earn more by law?

We do this is Europe, we pay something called 'kid allowance'. In some places people make 10 kids for the allowance, ignore them or mistreat them and live on that money.

Name one state where someone making minimum wage can afford an apartment, food, healthcare, and utilities, and some form of transportation. I think it's fair to say that if you can't, that counts as poverty.

Who says that's the point of minimum wage? That's where we disagree.

If you're agreeing that anyone living on that wage is in poverty, I think it's fair to call it a poverty wage.