Yeah, this seems likely to be true, and also arguably really sad, since it means your consciousness essentially is "dying" every second. Fun times!

Well, on the other hand, we are able to create joy and the rich array of emotions we feel through those moments, and against the scale of an eternal(well.... ish..) universe, creating joy for a future being is about all we have, whether that's an iteration of ourselves or someone else.

Then again, the last time I checked we don't actually know if time is quantized or not, or if that's even a meaningful question.

A slightly modified version of this idea is explored in https://existentialcomics.com/comic/1