iCloud keeps telling me to pay

1. iCloud does not backup computers. It can synchronize data from your computer if you store files in the iCloud Drive folder in Finder, or have the Documents & Desktop option turned on in System Preferences ➜ Apple ID ➜ iCloud Drive ➜ Options ➜ Desktop & Documents? Make sure it's unchecked if you don't want to use it.
2. If you have the Desktop & Documents option turned on (it had to ask you if you wanted to turn it on, and you had to answer yes for it to actually be on), it will automatically sync any files in those folders to iCloud.
3. It should not prevent you from storing anything locally if its on even if there is no space in iCloud, it may just state it cannot sync the files to iCloud for lack of space, but should still save them locally.
4. Are you sure you have a lot of free space on your hard drive? How much free space exactly?
5. You can manage the storage used in iCloud by following the steps here ➜ Manage iCloud storage on Mac - Apple Support

Yes, iCloud does save computer files, if you use Apple software (Pages, Keynote, Numbers, etc), but it also saves and syncs Photos, Messages, Notes, Reminders, Calendars, Music and stores device backups (unless you have turned off all these in each device's settings).

If it's just about saving Apple Documents using Pages, Keynote and Numbers, I would suggest making sure that their default save-location is locally, on your hard drive and not in iCloud.