Now it works but I am unsure why.
I did the following - maybe it'll help someone in the future.
I restructured the folder so all my raster types goes in C:\Program Files\ArcGIS\Pro\Resources\Raster\Types\custom\
Then I create a new mosaic raster dataset in my GDB with "Product definition" = "None".
When I then want to add rasters I can choose my custom raster data type.