Given as Caroline's first two marriages were to untitled men, I highly doubt she cared about Ernst's titles at all.
The Grimaldis are princes, yes, and they have a history of marrying individuals without titles. Caroline wouldn't care if her daughter married Georgi or some other prince (with or without a throne) or if she married someone without any title at all. The Grimaldis don't place any emphasis on dynastic marriages.
As for whether or not Caroline cared about if the throne if Hanover existed, I doubt she "went after" Ernst because of his higher titles - once again, her first two husbands were unable to provide her or their children with titles, so why would she care if her third husband came with a title?
And yes, the ranking of Royal Highness may be higher than the ranking of Serene Highness, but when you're the heir to throne that actually exists, even as just a Serene Highness, I doubt you'II consider yourself to be lower than someone who is the heir (or pretender) to a throne that no longer exists, even when they have a Royal Highness. Georgi might on one stand point be higher than Charlotte owing to his titles, but on another they're equals owing to the fact that legally neither of them actually holds titles (unless Russia's still legally recognizing titles), and on another she's higher because she might one day inherit (or even just be the daughter/sister of a monarch) a throne while it's unlikely that Georgi will ever do so.
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