What is the ruling on saying "God's providence saved so-and-so" or "Divine providence saved so-and-so," and is it permissible to utter it?

There is no harm in using the phrase "God's Providence" (عناية الله) as an informative statement about Him, the Exalted. Indeed, this is broader than being restrictively توقيفي (requiring textual proof) in the realm of informative statements. Scholars have used it without objection. However, the phrase "Providence rescued" (أنقذت العناية) or "God's Providence rescued" (أنقذت عناية الله) should not be used, because it attributes rescue to Providence, whereas it should primarily be attributed to God, for He is the One who willed and rescued. Thus, the correct phrasing is: "God willed," or "God's wisdom necessitated," or "God's Providence occurred/necessitated."