Unfortunately when notes are permanently removed by deleting from the Recently Deleted folder, they are not recoverable. It is that folder where they are saved for 30 days to allow to recover in case you change your mind.
As for your backup question, Notes that are synced to iCloud are not stored in an iCloud backup. The only time Notes are saved in a backup is when they are saved on your device, where you are not using iCloud to sync. Those Notes are in the "On My iPhone" section of the Notes app. The iCloud backup is overwritten whenever the next backup is completed, so that is not a good method to archive a backup from an earlier date. That can be done by using a computer to create an archived backup, and again the only thing backed up is the data on your device that is not synced to iCloud. More information about the backup options is available here:
In addition for a Note that you always want to have a copy of, you can use the Export option to save it as a PDF. Anything synced to iCloud uses the Recently Deleted folder to allow recovery for 30 days. There really is no need to delete anything from the Recently Deleted folder before that time unless you really want to permanently delete them.