Covered with solar panels and shaped into a giant flywheel?

Floating on the ocean catching waves.

Converting H20 -> H2 and storing it in fuel cells

With a heavy water thermonuclear reactor

Maybe the solution is using very dense material. Like nuclear power plant waste.

Or then we could use lot more of this pretty cheap, pretty available, pretty easy to handle stuff that we have mature technology and understanding for. Namely water. Only thing is that need nice reservoirs on top and bottom. The shaft it self can even be narrower and less sturdy...

No - it's just storing potential energy.

yeah this sounds like a pendulum but geared on the y axis instead of the x. in fact a pendulum seems more practical since it doesn't need a shaft, just an enclosure. I suppose a pendum is itself is just a special case of flywheel anyway.