How to download a land cover image using geemap?

Question

I am trying to download an image from gee using the geemap python library, from the Dynamic Earth land cover dataset for a particular lat/long.

However, I'm struggling using the geemap.download_ee_image() function as the land cover data is not stored in a single layer or as a ee.Image object.

I have been following this guide, but the input data don't seem to match up

Any ideas of what I could do?

Here is the code I'm trying to modify:

Map = geemap.Map()

region = ee.Geometry.BBox(-89.7088, 42.9006, -89.0647, 43.2167)
start_date = '2021-01-01'
end_date = '2022-01-01'

dw_class = geemap.dynamic_world(region, start_date, end_date, return_type='class')
dw = geemap.dynamic_world(region, start_date, end_date, return_type='hillshade')

dw_vis = {
    "min": 0,
    "max": 8,
    "palette": [
        "#419BDF",
        "#397D49",
        "#88B053",
        "#7A87C6",
        "#E49635",
        "#DFC35A",
        "#C4281B",
        "#A59B8F",
        "#B39FE1",
    ],
}

Map.addLayer(dw_class, dw_vis, 'DW Land Cover', False)
Map.addLayer(dw, {}, 'DW Land Cover Hillshade')

Map.add_legend(title="Dynamic World Land Cover", builtin_legend='Dynamic_World')
Map.setCenter(region)
Map