Not necessarily. Northern most part of Scandinavia have among the lowest prices for electricity in Northern and Central Europe. Most of the electricity there comes from Hydropower. It's also the same area where Sweden makes it green steel. Cheap and green electricity is not an oxymoron or impossibility.
Traditionally Swedish electricity has been about equal parts nuclear and hydro. Nuclear usually running full out, with hydro used to regulate for daily and seasonal variation.
In recent years they have built a lot of wind, as of 2019 providing 12% of electricity, today almost certainly more. But yes, like you said, hydro is used as the backup for wind.
