Is it possible to restore a Macbook from iCloud when Time Machine failed?

If you had Photos, files, contacts, notes, etc synced with iCloud you can turn on those options again and they will sync. If you aren't sure whether those options were on before the repair, use any internet browser and log into www.icloud.com -- the data that you can view there is synced.

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: 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

I backup to an external drive and I also sync my Photos with iCloud Photos (without the optimize storage option turned on so that I also have a local copy on my Mac) and I use Carbonite for the rest of my files. That way I have duplicate backups, one of which is offsite in the even of fore or theft destroying both my Mac and my external drive.