What is the ruling on supplicating for worldly matters only, and is it considered polytheism (shirk)? And when does saying, "Were it not for so-and-so," constitute major polytheism (shirk akbar)?

Supplicating Allah alone is legitimate and an act of worship. It is divided into Du'a al-Ibadah (supplication as an act of worship) and Du'a al-Mas'alah (supplication as a request), and both are intertwined, for Du'a al-Mas'alah is an act of worship to Allah. As for the saying, "Were it not for so-and-so, such-and-such would have happened," its ruling varies according to the intention of the speaker. If the intention is to attribute causes to other than Allah and to glorify them, then it is among the polytheistic utterances. However, if that is not the intention, but rather it is mentioned by way of causality, and the thing was a real cause, then there is no problem with it, and it is permissible.