This is going to be multi-faceted but it may work.
On your old phone go to Setting-->Accounts and Backup--> Backup Data and backup your device.
Also go to Notes-->Settings--> Sync to Samsung Cloud. ... If its already on turn it off and then turn it on again and it should sync immediately.
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On your new phone go to Settings-->Accounts and Backup-->Restore Data--> as long as you're signed into Samsung cloud you should see your old phone's backup... select it and restore all the data
Next, go to Samsung Notes-->Settings-->Sync with Samsung Cloud and turn it on. If its already on, turn it off and then back on again.
Hopefully, after that you'll have your notes back.