Deleting Old IPhone ICloud Backup

Hi, I just got a new phone and have run out of ICloud space, so I’m wondering what would happen to my old iPhone’s ICloud backup. My new phone shows as taking up more GB than my old phone, which makes me wonder if my old phone’s backup automatically became part of my new phone’s backup. If so, would everything from my old and new phone be able to move to my next phone if I deleted my old phone’s backup?