Your iPhone backups on your iCloud account are not related to your status in a Family Sharing group, other than your use of the shared iCloud space which a Family Sharing group provides. What is "it" which says that you can't access your iPhone backups?
In what sense do you ask about accessing these backups? They cannot be found as files to edit, but you can see the status of your backups, manage them, and see which of your iOS devices are backing up.
To see this follow the steps in Apple's support document View and manage iCloud device backups:
View and manage iCloud backups on your iPhone, iPad or iPod touch
On your iPhone, iPad or iPod touch, go to Settings > [your name] > iCloud.
Do one of the following:
- iOS 16, iPadOS 16 or later: Tap iCloud Backup.
- iOS 15, iPadOS 15 or earlier: Tap Manage Storage, then tap Backups.
You see the devices with iCloud Backup turned on.
To delete a backup, tap the name of a device, then tap Turn Off and Delete from iCloud (or Delete & Turn Off Backup).