When a Note is initially deleted, the Recently Deleted folder will appear. When all Notes have been removed from the Recently Deleted folder, this folder will cease to be visible - until such time as other Notes are deleted.
If you cannot see the Recently Deleted folder, any Notes within it have been irretrievably deleted from both locally cached storage and iCloud.
If you are using Notes in iCloud, as implied by your question (deletion having been synchronised with your iPhone), you Notes will not be included in an iCloud or iTunes backup. As such, you’ll not be able to restore your backup to recover [now deleted] Note(s).