When Ilya says "I could marry Svetlana" he's doing the exact same thing he did at the bar in Tampa.
At the bar, he asked Shane like three different questions trying to get him to answer his real question, "Are you and Rose Landry still together?" without having to actually ask that question outright. With each question, Ilya gets more pointed, closer to his real question, and each time, Shane doesn't pick up on it. Ilya is ultimately forced to ask his real question to get the answer he wants.
At the cottage, Ilya talks about wanting to get rid of his Russian passport and wanting American or Canadian citizenship. Obviously, marrying an American or Canadian would expedite this process. Ilya is hinting again. Hey, I want to talk about this with you, but I don't want to say it directly, because it might reveal too much or scare you, so I'm going to hint and hope you take the bait, essentially. Except, Shane doesn't realize it's bait. He doesn't realize Ilya is hinting at anything or trying to get Shane to bring something up.
So, when Ilya says, "I could marry Svetlana," he is being more pointed about it. Getting closer to what he's really trying to say.
Shane still doesn't get it, but Ilya gets lucky this time because the way Shane responds takes the conversation in the direction Ilya wants anyway.
Honestly, the first time Ilya tried baiting Shane with this same conversation was when Shane visited him, and Ilya said he was friends with this woman who was perfect for him, and that he thought he'd get married someday, but that he thought he'd find "someone else."
So like, literally just like back in Tampa, Ilya hinted multiple times, each time needing to get more direct before getting Shane to say what Ilya really wanted him to say.
It's such an obvious case of like...Ilya communicating in the roundabout way most people do, and Shane not understanding because Shane is not only very literal but also just so honest. He doesn't always say what he actually thinks - he stops himself from saying what he actually thinks with Ilya often - but when he does decide to say something, he almost always says what he actually thinks, what he actually wants to say, and it doesn't occur to him others don't.