I have been added to family sharing on ICloud
My sister added me to Family Sharing, but I still can't use iCloud as a backup, it always directed me to purchase a backup space
iPhone 11 Pro Max, iOS 15
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There are a couple of things to verify.
First, in setting up the family sharing group your sister would have sent you an invitation which you had to accept to join the group. See Set up Family Sharing. Get her to check on her device if you are a member of the group. There is an example on how to see this on the page I've linked.
It is possible that the iCloud space available to your family group is insufficient to support your iPhone backups to iCloud. Check which plan your group has. If it remains at the free 5 GB plan your sister would be well advised to buy one of the three paid subscriptions to ensure you have enough space for using iCloud. See iCloud+ plans and pricing - Apple Support.
What is "it" in your comment "it always directed me to purchase a backup space"?