Hello,
It seems the configuration and iCloud storage needs of the old phone do not work well with your new device. You have two options. One is to subscribe to more iCloud storage. See: Upgrade your iCloud storage plan - Apple Support
The other would be to Change your iCloud feature settings [iOS and Mac] - https://support.apple.com/HT207689 to work with reduced iCloud storage, or simply keep fewer items on your phone. Along these lines you could turn off optimization and/or iCloud backup and make sure you back up your iPhone regularly to a computer, plus transfer files to a computer. I have a 64 GB iPhone plus 4 other iPads and iPhones but I use less than 5 GB iCloud storage. How? I only keep about a dozen photos on my phone at any one time, I have few other things on the devices. However, many users would not like this solution so the only alternative if you are not a minimalist is to subscribe to more iCloud storage.
Also read: What's the difference between device storage and iCloud storage? - Apple Support