can you back up a Mac to iCloud?

How to back up your Mac - Official Apple Support

offers:

Store files in iCloud [not backup with Time Machine]

Use iCloud Drive to store and share files, and learn how to access them on all your devices.

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• Add files to iCloud Drive

See this article for Other ways to back up and restore files - Apple Support

Your only option is to sync Desktop and Documents folders in iCloud on the Mac. This is not a backup as it is just meant for syncing, so if you delete a file in one of those locations it will also be deleted in iCloud. The location to find this setting is  > System Settings > [name on top] > iCloud > iCloud Drive > Desktop & Documents Folder.

You do need to have a backup and Time Machine is one option that works automatically and very effective. To use this you would need to buy an external drive and connect it to your Mac. There are many options for an external drive and maybe some other users could provide some specific manufacturers to recommend to help you get this set up. There is also the NAS option to backup wirelessly.

Backup disks you can use with Time Machine - Apple Support

No; if desired, you can manually sync or upload content to it, but it's not intended for Mac backups.

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It's an interactive service that mirrors changes you make locally. So no, iCloud will never be a longterm full detailed backup as files come and go as you direct.