iCloud backup from old phone showing on new phone

I currently have 200GB of iCloud storage shared for me and 3 other family members. I'm getting close to the limit. Today we upgraded my son's iPhone. He signed out of his iCloud account on the old phone. When he goes into iCloud on the new phone and looks at the iCloud backup area he sees the old "iPhone 12 backup" and there is no new backup for the new phone. Is this because there isn't enough remaining space in our 200GB space? Should he select the "iPhone 12 backup" and delete it? Will the new phone then begin backing up? When I look on my phone I see in iCloud+ the following: 176.4 GB of 200 GB Used. When I go to Family Usage I see he is currently using 47.3 GB. I've tried to google this but not having luck. Hopefully the community can help.