How do I get what I backed up onto my new phone?

See the following Apple Support article for information on using an iCloud Backup to setup a new iPhone: Transfer data from your previous iOS or iPadOS device to your new iPhone or iPad - Apple Support

Another option is to use Quick Start which is also described in the same support article.

When you're setting up your iPhone there should be an option to restore from a backup.

Here's an article --> Restore your iPhone, iPad, or iPod touch from a backup - Apple Support