As with angels on the head of a pin, the interesting argument is whether the amount of compute is finite or not, not how finite it is.
And, considering the visible universe is also finite, with finite amounts of matter and energy, it would follow ultimate compute quantity is also finite, unless there is an argument for compute without energy or matter, and/or unlimited compute being made available from outside the visible universe or our light cone. I don't know of any such valid arguments, but perhaps you can point to some?