Yes, when it comes to total energy production, we do have a lot of oil and gas - but that's mainly being sold / exported. Hydropower is by far the leading energy source for production of electricity - Seems like in 2020, 1.3 TWh of our electricity production came from natural gas - while 141 TWh came from hydropower. Wind at second place with 9.9 TWh.
Now, all energy production (AFAIK) here is owned by the Norwegian Government. So high exports would naturally mean more money to Norway - which they then "pay back" to the people by subsidizing high utility / electricity bills in unprecedent times like these.
The crux is simply that people in Norway have been used to very low electricity prices, for pretty much forever now. Seeing your bill increase by 3-6 times (even after the subsidies) has not been popular - especially not since many feel that this situation has been artificially created by the energy actors.
Worst case, we sell all our reserve electricity because prices are high, and experience rolling blackouts if we can't import enough come winter.
EDIT: In the first link you posted, you can see in the graph there's one indicator named "Electricity generation by source", you will see that Hydro absolutely dominates Norwegian electricity production.
Other countries are much more diversified in that area, but also considerably exposed to natural gas - which seems to be the driver behind this crisis, as there's a shortage in exactly that.