Hi! This is a great question. My name is Lena and I work on Voltaire and his library. Here are some examples from their correspondence of Catherine's favourite works by Voltaire, by no means an exhaustive list (she specifically ordered that all of his published works be sent to St. Petersburg along with his private library after his death). One would have to do a bit more digging to see her letters specifically to other Russian nobles, but I would hazard a guess that she did not keep these works to herself :-) She also admired Montesquieu's Esprit des Lois and used it in drafting the Nakaz, Russia's reformed legal code (which she then sent to Voltaire for feedback).

• September 16 1763 CII writes to V: "By chance your works fell into my hands, I could not stop reading them, and I wouldn't want book that wasn't as well written, and from which so much could not be profited."
• June 1765: Looks like Essai sur les mœurs was a big one: "She [CII in 3rd person] has read this great book from one end to the other with much pleasure...She is persuaded that this book will prove her thoughts, it will be purified by fire, in Paris, which will give it an even greater shine."
• October 17 1771: Questions sur l'Encyclopedie, in particular the article on fanaticism, "which I read with the greatest satisfaction in the book of the Questions sur l'encyclopédie."

If you have a university subscription, I would recommend searching through their correspondence on Electronic Enlightenment. Ecrasez l'infame!