My photos do not appear on my new phone. I backed them up to iCloud and restored on new phone but they are not there.

Go to Settings/[your name]/iCloud and turn on the switch for Photos.

iCloud+ has 2 independent functions. iCloud backups, and iCloud sync. It’s confusing because they both have the same name prefix. But they have no connection with each other. Go to Settings/[your name]/iCloud. You will see a bunch of switches. When you turn on a switch that data type will sync to iCloud. If you do this on multiple devices that share an Apple ID the selected data will sync to all of those devices. 

You can also turn on iCloud Backups. This will back up your phone every night if the phone is plugged in, connected to Wi-Fi and locked.

But note that anything that you sync by the first method will be excluded from the iCloud backups, and cannot be restored by restoring a backup. It can be restored by turning on the same switches you had enabled previously.