"Mushroom hunting" is a fairly common phrase in English, too. It appears to have the top-level title for the page about that activity, on Wikipedia, even (mushroom foraging, mushroom picking, and mushrooming are all given as alternative terms)
Plus it's the title of a song on the Cowboy Bebop soundtrack, so it has that going for it.
The German term is "Pilze sammeln" which literally translates to: collect mushrooms.
There are many dialects of the German language - where I'm from, we would use "Schwammerl suchen" ("Schwammerl" as another term for "Pilz(e)"). This literally translates to: searching for mushrooms.
"sammeln" can have multiple translations. "Collect" would be more like "einsammeln". In the context of "Pilze sammeln", you'd use "forage". You forage for food.
Plus it's the title of a song on the Cowboy Bebop soundtrack, so it has that going for it.