New Apple ID - Cannot re-download purchased app

Those purchases are tied to the other ID and can't be transferred. One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID. 

Purchase History Review.   

Or you can try to set up Family Sharing  between the IDs to keep access to your purchases.

Family Sharing.         

Family Sharing - Set up.        

Maybe I am not understanding what you are seeing, but if you can download the apps using the old ID, what is preventing you from doing that? The cloud logo is probably there because you are logged in with the new ID, so the apps won't download using the new ID.

The link worked properly for me.