Putin doesn't care one iota about the Lord of the Rings Western non-sense. In fact, most of the people around these parts of the continent (Eastern Europe) don't care about the novels themselves, apart from a very thin layer of the Westernised middle-class (I'm part of that Westernised middle-class layer and I don't care for the books, the movies were interesting for an one-time viewing 20 years ago).
But, yes, people from the West will always make everything be about them.
Later edit: If anything, it is Tolkien who has borrowed "the giving of expensive jewellery as an act of power" from Tsarist Russia, see articles like this one [1] about how 19th century Russian emperors were delighted in making such gifts. If anything, Putin wants to be a 19th century Russian emperor, again, he doesn't care at all about Western-created stupid memes.
[1] https://www.thejewelleryeditor.com/jewellery/article/as-the-...