The standard Apple Notes apps will back up any notes taken to iCloud automatically, as long as the settings are configured correctly here: Backing up data to iCloud
If you are using any other non-standard apps that were self-installed, you will need to configure settings manually for each app. For some note-taking apps, notes backup will need to be done individually, as the app is currently not configured to backup to iCloud automatically.
Do refer to these links to learn how to backup data for the various apps.
For Notability backup:
https://support.sluh.org/notability_backup
For Kilonotes backup:
https://youtu.be/fYWkKdf-ZrE?t=456
For Collanote backup:
https://collanotewiki.github.io/en/pages/FAQ/How-to-backup-Notes-and-PDF
For Goodnotes backup:
Open Goodnotes, tap the ⚙️ icon in the top-right corner of the Library view > Cloud & Backup > Cloud Storage and enable "Use iCloud to Sync Documents".
https://support.goodnotes.com/hc/en-us/articles/7353703842831-Check-for-a-backup-of-your-Goodnotes-library-in-iCloud
https://support.goodnotes.com/hc/en-us/articles/7353694866831-Back-up-and-restore-your-library-manually
For Sketchbook backup:
https://help.sketchbook.com/getting%20started/file-saving?from_search=189814585#saving-in-sketchbook-for-ios-6
For Procreate backup:
https://agfdesignstudio.medium.com/how-to-backup-your-procreate-art-ipad-2273e8727f3a