Answer the question. Why do strong welfare states have low poverty rates, and when Manchin blocks bills, is that the fault of the Democratic Party as a whole, or the backwater states that elect them?

I suggest you research more rather then just looking for examples that only prove your point

You should take your own advice. I gave you 6 via the Wiki page. You looked for examples to prove your point, and all you found is one 20 year-old study, not to mention it's limited to immigrant households.

Which is more important to the reduction of poverty? Economic growth or welfare?

Welfare by a mile. The US is the biggest economy in the world, and yet so unequal, which is why there's so much unrest and crime.

On the other hand, UK may not be as big as the US, but at least they don't have people having to choose between life-saving medicines or not contacting an ambulance because of the exorbitant, frankly-surreal-for-a-developed-country healthcare costs in America.