If setting up a new macbook from an icloud back up, will applications be set up too?

There is no option to set up a new Mac from an iCloud backup.

If you have a Time Machine backup to an external drive, the following may help: Transfer to a new Mac with Migration Assistant - Apple Support

Apple offers iCloud Backup for iPhones and iPads but not for Mac computers.

It is possible to sync data from a Mac to iCloud if you turn on those options (e.g., iCloud Photos, iCloud Drive including the Desktop & Documents option). Syncing has some of the benefits of a backup (and the benefit of being offsite) but is not the same as a backup. Major differences include the fact that not everything on your Mac can be synced and the fact that if you delete something, accidentally or otherwise, there is only a limited time period (30 days in most cases) during which it can be recovered.

Also see the Apple article: How to back up your Mac - Official Apple Support

And more information on syncing in:

Set up and use iCloud Photos - Apple Support

and

Access and manage your files in iCloud Drive - Apple Support

and

Add your Desktop and Documents files to iCloud Drive - Apple Support