Export raster data to specific epsg code gives out black image

Question

• new project
• define coordinate system (in my case epsg 25832 (UTM 32)
• import raster data (in my case .jp2 image)
• right click -> export the layer which has the image
• Format GeoTIFF and now the problem: if I choose the coordinate system epsg: 5682 my image will be blacked out if I choose another coordinate system epsg: 5683 it will export just fine

the problem is epsg: 5682 is the right zone in that specific coordinate system, i can not just simply choose a different zone or a different coordinate system, it has to be 5682... How can this happen?

The specific image can be downloaded on this government website: https://www.opengeodata.nrw.de/produkte/geobasis/lusat/akt/dop/dop_jp2_f10/

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