I know very little about Catherine the Great, but I know a lot about bananas - I am the author of “Banana: The Fate of the Fruit that Changed the World,” which some consider to be the definitive history of the fruit. Catherine reigned in what is now (mostly) Russia in the mid to late 18th century. So let’s break this down.

1. Would she have known what a banana was? This is pure speculation, but I’d say possibly yes. Catherine’s lifespan dovetails - almost - with the craze that swept sectors of European nobility to collect exotic fruits. A network of fruit hunters and traders brought seeds (and in the case of bananas, which are mostly seedless, cuttings) to their patrons. For example, William Cavendish, the sixth Duke of Devonshire, began growing bananas in his greenhouses in 1834. His banana, the Cavendish, is now the world’s largest banana crop; it is the one we eat in the US and Europe. Cavendish was a little after Catherine’s time, but given that Linnaeus described bananas in the mid-18th century - his life spanned roughly the same period as Catherine’s - it is possible that she’d heard of the fruit.

2. Having heard of the fruit, would she have tasted them? Somebody better versed than me in Catherine’s movements would have a better answer, but she is associated with a vastly increased interest in Russia being part of European culture, and she (and the rest of the Russian elite) had many interactions, familial, cultural, and commercial, with Western Europeans. But were bananas part of that? The answer is possibly, possibly not. The problems facing anyone who wished to eat a banana (right up until the 1870s, when banana commerce began in earnest) is the issue of transportation. Bananas are fragile and don’t keep well, and they need to be shipped quickly and under refrigeration or in cold chambers packed with ice. The closest places bananas were grown to Russia (with the exception of possible greenhouse plants) would have been the Middle East, maybe the Canary Islands, maybe Northern Africa. All pretty far away. There were bananas (and plantains) being grown in colonial South and Central America at this time, but even there, there were little to no mechanisms for bringing bananas from those places in any way that would allow them to arrive fresh and edible to Moscow or other cities on the Russian interior (or pretty much any European city, with the possible exceptions of places like Lisbon. Barcelona, and Marseilles.) That said, bananas are very easy to grow from cuttings, so it is possible that a cutting could have been transported to Russia and grown indoors there.

3. Finally, there’s this: bananas - I’m not joking here - were considered taboo, especially for proper ladies, because of their shape. Early cookbooks and food preparation guides suggested that to be served with propriety, bananas had to be cut so they no longer resembled what we all know they resemble. As most of us also know, a cut banana isn’t going to keep very long. However, and forgive me for implying a moral judgement - no such implication is meant - Catherine was not what the Victorians would have considered a proper lady. From what I understand, she enjoyed a rather active sex life, and had multiple partners. I suppose, then, that it is possible that the taboo of the banana, rather than repulsing her, may have attracted her (to sell bananas to less free-spirited American women a century later, the banana companies produced postcard showing elegant women, often at picnics or other social events, pressing the fruit to their lips. Again, not joking.)

Reminder: all this comes from a banana person, not a Russian history person, so please forgive and correct any errors on that side of this response.

You might also like this answer from /u/Dicranurus about banana consumption in Russia in the 1800s.