“However, they DID NOT advocate the welfare state, with Robin Hood-style economics and a paternalistic state doling pout welfare to the orphans and widows.”
No, but Torah and Chazal did. Communal authorities are required to provide for the poor, even levying taxes to do so.
The mitzvot that Chazal singled out that are to be taught to prospective converts are not Shabat, kashrut, and taharat hamishpacha — or even the prohibitions against abortion or homosexual sex — but leket, peah, shich’chah, and maaser oni. The reason is simple as I once heard from Rabbi Dr. Moshe Tendler: Non-Jews need to learn that their belongings are not theirs in the Torah world. Everything belongs to God and we are commanded to share and not be resentful about it. In the shemittah year anyone can come into your field and pick fruit from your orchard. In the pilgrimage festivals anyone can show up at your doorstep and you have to let them sleep in your bed. There is no such thing as permanent land ownership in the Land of Israel outside of cities. Overcharging and undercharging in business are prohibited, and when the communal authorities levy taxes for the poor, for education, for health, or for public works we pay them. This isn’t socialism, but it isn’t laissez-faire capitalism either.