I'm backing up all my files on iCloud (I think). If I need to access my backup from another Mac, how do I do that?

Apple offers iCloud Backup for iPhones and iPads but not for Mac computers. However if you are syncing data from a Mac you can log into www.icloud.com from any computer, including your other Mac, to access the data.

Note that 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

iCloud Drive FAQ - Apple Support

See the articles https://support.apple.com/en-in/HT204350

https://support.apple.com/en-in/guide/imac/apd6a937e818/mac