I do not know. We don’t understand how the world works. Perhaps there is a universal bank of information, for example, it can be stored in the arupa-spheres, in the sphere of infinite consciousness. but our individual consciousness is unequivocally impermanent. The better something is stored, the more lifeless it is. For example, information about the shape of a stone is stored for millions of years, especially since it is lifeless. The more life there is in the being, the higher the speed of processes, impermanence, and so on. The most permanent is nirodha, the cessation of all processes. From that nibbana is eternal, that it is a cessation without re-emergence. Therefore, to compare the bank of information storage, traces of the past and consciousness, I think, is not correct. They have different functions. Traces, it seems to me, are stored in the unconscious, in the field of samskara. Samskara by definition is formation. And close to the meaning of the word - information.
For countless lives.
Buddha remembered so many lifetimes and he didn’t get to the beginning where this process started. And this process most likely once began, because something that has no beginning, did not arise once - cannot even exist. The Suttas bypass this point, as they believe that the Buddha was omnipotent as God. But he never claimed this. The powers of a Buddha have some natural limit, as does the ability to remember. For example, not all yogis can remember many hundreds of lives, others get only 3 or 7. why? because the further you go, the less clear the information will be. Erasure happens one way or another. The deeper a yogi penetrates into the subconscious, the less there is from consciousness, and more from static lifeless formations that are like hard diamonds.
By the way, information can be overwritten from device to device for a long time. Information is not equal to the medium on which it is recorded. But with the cessation of the carrier, the information also ceases. However, all samskaras must be lived out and erased before awakening.
My theories about individual memory do not explain, however, how the Buddha saw the past lives of other Buddhas. This information is definitely stored somewhere, but not in the individual consciousness. And consciousness, as we have already determined, this bank of information cannot be called. An active process of life and knowledge is one thing. The other is a frozen, cold, frozen preservation of the imprints of past formations, relationships, and so on.
Perhaps the consciousness of the Buddha penetrates the level of the space-time continuum and sees the chain of events as the fourth dimension.