First of all, a clarification: Love's Heart is not on Steam and won’t be, because it was rejected. The game that is on Steam—and has just been released, in fact—is United by Love's Heart.
Answering your question, no, of course, you don’t need to buy it twice. If you buy it once on itch.io or on Steam, I’ll keep updating it on those platforms.
However, let me give you a recommendation: with how badly itch.io is treating game developers, I suggest you buy it on Steam and not here, because I can’t guarantee that in the future itch.io won’t unfairly ban my game here, preventing me from continuing to update it.