that depends hugely on how you interpret what is ‘carried over’ during rebirth. In Buddhism, about which I know the most but ultimately am no expert, it’s always in change, like everything in buddhism. Every day millions of creatures die, some to be reincarnated as the same thing, some as something different not at all present in our corporeal realm. Pure Land Buddhism might feature one of the more recognizable manifestations of this, plastered all about the country.
南無阿彌陀佛 - a nenbutsu or nianfo (japanese very influential in this particular branch) which are often used for recitation, chanting, and meditation, but in the case of Pure Land Buddhism ala Honen, making a regular practice of saying this while would permit one to be whisked off to a Pure Land, which is itself… well, it’s kinda like going to a buddha or bodhisattva’s personal little bubble of happiness, in this case Amita buddha’s, where you’ll have a generally pretty good time and be surrounded by bodhisattvas and all that can help you reach enlightenment. This is just one of many non-corporeal realms, others including being reborn into godhood (desirable but ultimately not nirvana and the chill lifestyle there will bring you back to human eventually); conversely, there are animals, hungry ghosts and the hell realm. And you could spend a very long time in any of these realms. Especially the god and pure land realm.
Now Buddhism rejects the existence of a soul but generally believes in some sort of carry over from one life to another. It’s not your self, your soul, it’s more like… a giant pan-living consciousness, and by your actions kinda provide a general kick in the direction of where you will go next, but ultimately you can life an awful life and it can take an indeterminate amount of time to move them to a different plane of existence. Eventually karma will take it’s course, but mostly it just loosely casually links lives.
It’s also worth noting that humans are probably the most capable of movement; animals live short times, comparatively, generally, but have no real ability to act according to buddhist precepts, and therefore maybe spend more time in the animal realm hopping about from life to life, thereby balancing the life balance overwhelmingly in favor of animals. But the same can basically be said for any plane that’s not human - the gods are too comfy and chill to care about working towards nirvana, the hungry ghosts are pretty pitiful and driven exclusively by desires and suffer immensely because of them, etc. We humans are the most capable of engaging with our own desires and the religion and thus, it would stand to reason, have the best chance of moving around the spectrum because we have full responsibility and authority over our actions. But this is just speculative - I’m no expert.