The only example that I know of is Norway which is kind of the holy grail of hydro, in general:

1. Small population.

2. Pretty tall mountains and sparsely populated mountains (see 1.)

3. Quite high yearly rainfall levels.

4. Very rich country.

5. Country with a very low level of corruption and from what I know, pretty efficient at building new infrastructure.

Is there an example of an "average" country having decent levels of pumped hydro storage at a level that's above 0.5% of the country's needs?

The UK has had pumped storage since 1963, there are more planned around the world - this is neither exotic nor particularly hard, the only constraint is land, and as I mentioned there are multiple other solutions.

Scotland has already entirely met its needs with renewables this year. This can and will be expanded to other nations in time.

Oh, just a few oddballs nobody's ever heard of: Switzerland, Austria, Portugal, Japan, Spain, Italy, South Africa, Belgium, Ukraine, South Korea, Poland, France, Australia, Thailand, Germany, UK, India, US, China, Russia.

According to https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricit...

That's power, not energy.