Is marrying a second woman considered an establishment of a Prophetic Sunnah if a man intends that, or is it permissible like eating and drinking, and not considered an act of worship?

There is no specific prophetic tradition (Hadith) that encourages polygyny. Rather, the Hadiths that encourage marriage in general apply to it. Its rulings vary between being obligatory, recommended, and permissible. There is nothing that makes it a permanent Sunnah, but one who practices it with a good intention, such as increasing progeny or providing chastity and care for another wife, will be rewarded for it.