Learn Turkish: Yaklaşık üç dört adet topladım ve kavurdum. - I picked approximately three or four pieces and roasted them.

In Turkish, you can express an approximate number simply by placing two sequential numbers right next to each other, like üç dört (three or four) or beş altı (five or six). You don't need to use veya (or) between them.

Isn't using yaklaşık redundant if üç dört already means "three or four"?

It might feel a bit repetitive in English, but it's very common in Turkish! Adding yaklaşık (approximately / about) before sequential numbers just gives extra emphasis to the fact that this is a rough estimate.

What does the word adet do here? Could I leave it out?

Adet means "piece" or "item." In Turkish, it is frequently used as a counter word after numbers when talking about physical objects. While you could technically drop it and just say üç dört topladım (I picked three or four), including adet makes the sentence sound much more natural, similar to saying "three or four of them" in English.

Why doesn't adet have an accusative (direct object) ending, since it's the thing being picked and roasted?

Because the "three or four pieces" are indefinite. You aren't talking about the specific pieces you previously mentioned, just some pieces you found. In Turkish, indefinite direct objects do not take the accusative suffix; they stay in their bare dictionary form.