Hi faeded,
Thank you for participating in the Apple Support Communities. It appears that you're missing some notes and folders, so we'd like to share some resources with you.
When you create an iCloud backup, "it only includes information and settings stored on your device. They do not include information already stored in iCloud such as Contacts, Calendars, Bookmarks, Notes, Reminders, Voice Memos4, Messages in iCloud, iCloud Photos, and shared photos", as quoted from: What does iCloud back up? So to answer your question, performing an iCloud backup will not include or replace any data currently syncing to iCloud, but it also won't necessarily be what brings back those notes and folders that suddenly disappeared from your device either.
Let's see if we can figure out why some notes and folders are missing on your device, even though they show up on the iCloud website. If you're seeing the notes and folders on the iCloud website, that means they are in iCloud but they just aren't making there way down (syncing) to your device. So, even though that data is syncing to iCloud, it still requires enough available device space to store on your device. With that said, let's confirm you have enough free space available for your device storage. This article will guide you through that: How to check the storage on your iPhone, iPad, and iPod touch. If you don't have much storage space available, this could be the cause for the issue you've noticed. If that's the case, check out the suggestions in that article for managing your existing storage.
If you're missing notes on your iPhone, iPad, or iPod touch will walk you through checking the Recently Deleted folder and other folders in the Notes app, too. If you find the notes you're looking for tap Edit, select the note, tap Move, then select the folder you want to move it to.
If the issue remains, tell us if there is any other content in iCloud that is not syncing to your device, besides notes. Are you noticing these notes and folders missing on any other devices that are signed in to the same iCloud account?
Reply if you need more help.
Cheers!