You can load the map in QGIS using Web Map Service (WMS). In the browser-panel, right-click WMS, add a name and the following URL: https://services.bgr.de/wms/boden/buek200/?
Than close by clicking OK. Now you have a new WMS-connection that you can expand. Select an item and drag and drop it to your layers-panel and the map will load: see screenshot:
Select 3857 as project EPSG (bottom right in your QGIS-window, see following screenshot). Select different layers for the different regions that are available. If you have a basemap like OpenStreetMap in the background, you can also apply layer blending modes to see both maps combined - I used multiply as layer blending mode, see screenshot here.
In the product center you can also load the product info-sheet as pdf with detailed information and meta-data as well as contact-information. As far as I can see, there is only access as WMS available, that means you can load the image via this web-service in your QGIS window, but there is no way to safe the data locally on your computer. Distribution as image-file (png, jpeg, gif) mentions n/a (not available). So if you need the data for more than just viewing and inspecting in QGIS, I guess best is to get in contact with the data-owner with the contact information provided in the pdf mentioned above:
However, you have the data available also as ESRI ShapeFile, thus not as image, but as vector data - this is what you can use to work locally. Download form here: https://download.bgr.de/bgr/boden/BUEK250/shp/buek250_mg_utm_v55.zip
Just unzip the downloaded folder and add (e.g. by drag and drop) the shp-File (buek250_mg_utm_v55.shp - the largest file) to qgis.