The concept of a freshwater sump, is no different than a salt water sump
Ammonia and nitrite consuming bacteria use and detoxify those chemicals, and their population will coinside with the waste output of fish, and other metabolism in your tank.
Plants will consume some nitrate, and other nutrients, if you have enough of them.
To consume all the nitrate produced by fish, you will need at least 10 times by weight the amount of plants, compared to fish.
Much like a saltwater sump/refugium there are animals that can be added to a fresh water refugium.
In a salt version you might use lots of marine algae like caulerpa, or mangrove trees, and may also use marine shrimp.
In fresh water there are even more plant possibilities, because there are terrestrial, semi aquatic and aquatic, I use all three.


Above terrestrial and semi aquatic plants in the main tank.
Below my sump filled with submerged aquatic plants like Vallisneria and hydriilla

But also like to add known nutrient users like salviina, lilies, and even mangrove trees, the sump above has about a dozen mangrove tree saplings.
Once a tank is completely cycled, I don't concern myself with bio-media, because evert surface (including plants) becomes a biofilm-bacteria substrate.
I also use a population of shrimp in the sump to help break down, melting plant parts into more useable substances by plants, and any fish foodr that might over flow into the sump .