Depending on how many apps you have set as backing up in each iCloud backup it may take up more space than available. You can see what apps are taking up the space by going to manage storage.
I do my backups locally, using iTunes to back my 13 up to the PC. Then the PC is backed up weekly to an HD that is kept in a fireproof safe. I feel more comfortable keeping backups local, and not in the cloud - just a suggestion. 😊
It needs enough to back up everything selected, or it won’t start. I’d suggest buy more storage, at $12/year for 50GB it’s cheap insurance. Otherwise, Settings > {name} > iCloud > iCloud Backup see if you can turn off enough items to get it under ~2.2GB (you might not be able to, as some items can’t be disabled - e.g. Messages).
I do my backups locally, using iTunes to back my 13 up to the PC. Then the PC is backed up weekly to an HD that is kept in a fireproof safe. I feel more comfortable keeping backups local, and not in the cloud - just a suggestion. 😊
It does seem somewhat odd that you have 2.2GB left, and now you suddenly don't have any space. Did you happen to download a large file, or record a long video since the last successful backup on 19 March 2022?