Accessing and deleting old iPhone's iCloud backup after factory reset

Ive just sold an iphone that was backed up to my apple id icloud and before giving the phone i logged out and factory reset it.

on my new iphone i logged in and seen that i was still logged in on that old phone so on the new device i logged it out.

ive accessed my iCloud storage and i have the old iphones back up there but cant view anything ? Have I limited my access ? Can I delete that back up now and because im logged into my original apple id on the new phone and ive backed it up i wont lose anything that maybe be on the back up of the first iphone ?

[Re-Titled by Moderator]

Original Title: data back up