How long would it take for a rogue planet to evaporate in the late stages of the Universe?
Before the evaporation of black holes that you mention, our universe will enter what is known as the Black Hole Era. About $10^{40}$ years from now, all the protons and neutrons in the universe will have decayed into positrons and neutrinos. This is how the last of the planets will pass away.

The Black Hole Era is so named because at this point only black holes and elementary particles will remain.

It should be noted that there is currently no evidence for proton decay, and so this phase of the Universe is strictly theoretical.

Source:


The Decay of Heaven - DeepAstronomy.com