Samsung Notes is the new option and should have backed up in Samsung Cloud and transfer across.
Maybe the issue is you have the older version so are you able to update to Samsung Notes on your previous phone ?
Samsung Smartswitch maybe another option to try.
That or manually re-enter your notes which I know can be a slow and tedious option.
I wish you all the best with this.
Current Phone ~
Samsung Note 20 Ultra 5G SM-N9860_256Gb SnapDragon 865+
Samsung One Ui 3.1/ Android 11.
@Tanzmenagerie: Can you try opening the Samsung Notes app via your Apps menu > Tap the 3 lines in the top left > Tap the cog in the top right of the pop up window > Import Data > Memos > From Samsung Account, to see if you're able to recover your backed up memos in this manner?
I too have the A3 and came across this thread while looking for a memo transfer solution. What I intend on doing is to email the memos to myself and then copy and paste the content into whatever Memo/Notes option is available on the Samsung A32. One step better than creating new Memos/Notes from scratch.