Is it possible to know how long a nuclear reactor has been running in Civ 6?

Solution 1:

Yes, it is.

When you move your mouse over the "Recommission Nuclear Reactor" option, you'll see a tooltip, where the "Reactor Age" in turns can be seen.

Note that recommissioning a Nuclear Reactor will reset its age to 0.

"Recommission Nuclear Reactor" tooltip screenshot

In this case, the reactor's been running for 84 turns since it's been built or recommissioned.