iPhone backup and cloud storage space question

Yesterday I bought a iPhone16 to replace my iPhone SE 3rd gen (which I'm keeping for now). I only use the free 5GB iCloud storage because I don't keep much on my phone. My contacts/photos/notes/drive/messages are saved to iCloud, and I have iCloud Backup turned on.

The guy at the Apple store said I would have to transfer the data from my old phone to new phone at home because I did not have enough storage in iCloud, and the data on my phone was too large. That wasn't a problem - I did that and everything transferred over fine, including all my apps and their data.

My question is that the Apple guy insisted I needed to pay to upgrade my storage because I have more than 5GB data, and I wouldn't be able to restore from a backup (thus requiring the phone-to-phone transfer). Although my new phone is set up now, I want to be sure that if it's lost/stolen/broken I'll be able to restore a new device from the backup since I won't be able to do a phone-to-phone transfer.

On the old phone that he was looking at, it showed the following:

• iPhone storage: 42.3 GB of 128 GB used
• System Data: 11.53 GB (this is what he was pointing out to me as being too big)
• iCloud storage: 3.1 of 5 GB
• iCloud backup: 1.3 GB

The new phone is basically all the same except that System Data is only 5.92 GB. I assume the difference is in cached data and logs, which were not transferred to the new phone?

Was the Apple guy right or wrong in telling me I needed to upgrade my storage? Between the backup and iCloud sync, would all my data be available if I needed to restore to a new device without access to the current one? I do want to be sure that my app data and settings are backed up and can be restored. Everything else I either copy to my computer or don't care that much about.