If I add storage and plan to buy a new phone in a month can I transfer the storage?

Yea iCloud storage is virtual on Apple servers. These resources below will give you more information on iCloud storage with your Apple accounts.

What's the difference between device storage and iCloud storage?

https://support.apple.com/en-us/HT206504

Manage your iCloud storage

https://support.apple.com/en-us/HT204247

iCloud storage is attached to your iCloud account, not a specific device.

Therefore your storage is available to all Macs, iPhones, iPads, and other devices associated with your iCloud account.

There is no option to directly add additional storage to any iPhone.