It raises an interesting philosophical question - where does all the energy of the spinning motor "go" over the billions of years?

Since energy can't be "destroyed", and all energy eventually degrades to heat (entropy and all that), the heat will dissipate over the trillion years.

If moving the final gear is the sum total of all the energy put into the system, it's essentially all gone at the end.

So - is there any energy left at the end to move the final gear?

Am engineer.