Will deleting all info on my old iphone affect my new iphone information?

I bought a new iphone and need to delete everything on my XS Max before sending into carrier for credit towards my new iphone.

When I purchased the new iphone I used my appleID and everything transferred. The one issue I am seeing is the new phone cake with 3 months free of music and arcade. Why am I seeing this info on my old phone too?

Thats why i’m concerned about deleting everything on my XS Max .. Somehow I feel it is connected to the 13 pro max.

The other thing that i’m concerned about is that when I go to delete it says my spectrum tv and 78 other apps need to be backed up.

I don’t understand because it said my phone backed up at 4:30 am.

Please if someone can tell me it’s ok or it’s not ok to delete and reset my old iphone I would so appreciate. I need to send this phone in by tomorrow Wednesday 10/27/21. Thanks in advance!