Your best bet would’ve been to copy the files from your original sd card to the new one once it was formatted.
Currently the system transfer option preps the data to be sent to a different 3ds in tandem with it that becomes associated with those games etc preventing the first 3ds from using everything that would now be on the 2nd 3ds.

You may or may not be able to log into the store on your 3ds using your same account and download your games, use the newer sd card and don’t copy the stuff you backed up onto it beforehand. Personally I haven’t messed with backing up just your game saves, but you may be able to take the saves from your backed up files and use them. IMO read up on savefiles if you get this far.