To switch from one iPhone to another, you should back up everything to your iCloud account and then restore it on the new iPhone.
Changing physical SIM cards on your phone is always a fiddly business. First, you have to root for the little SIM tray tool that Apple includes in the box with its new iPhones – except those in the US ...
You can turn off data on an iPhone all at once, for specific apps, or by turning on Airplane Mode through the Control Center.
If your new phone no longer supports SIM cards, or you don't want to use them anymore, you can convert to eSIM instead. I started my career with CNET all the way back in 2005, when the (original) ...