Unless we're proposing it to be infinite, I'd guess Sundar Pichai's last generation data center could handle the volume, but I agree with the others that that my consciousness would not be stored in a recording.
Of course, there is tomorrow.
Not any time soon.
Each of us knows far too much to be encoded without vast, vast, vast, amounts of storage.
Technology can only replicate the linear logical masculine aspect of consciousness, not love or the non linear emotional feminine aspect of consciousness.
The human soul has both masculine and feminine aspects of consciousness, held together and stabilized by love. Memories are stored in a physical field surrounding the physical body in holograms at the intersection of these two aspects of consciousness.
Gender identity is a function if the dominate aspect, regardless of gender.
These are all physical to me.