Hello allison_burger,
Thanks for updating us with that information.
To check if the restore process is still working, go to Settings > [your name] > iCloud > iCloud Backup on your new iPhone. If your iPhone is still being restored, you should see a message stating that and may also see "Stop Restoring iPhone" shown.
If that is the case, we'd recommend leaving the iPhone connected to Wi-Fi and charger for a while to allow the process to complete. This typically only works when the iPhone isn't in use, so most people don't notice this occur if they have the iPhone plugged in overnight with Wi-Fi. The amount of time taken for the process to complete depends on the amount of data and network speeds, so this can vary.
Check out the following resource and info for more details on this, and let us know what you find: About missing information after you restore your iPhone, iPad, or iPod touch with iCloud Backup - Apple Support
About your Messages and Voice Memos data
With Messages in iCloud and Voice Memos in iCloud, your text messages and voice recordings automatically upload to iCloud. They aren’t included in your backup. After you restore your device from iCloud Backup, stay connected to Wi-Fi so that your text messages and voice recordings can download.
If you turn off Messages in iCloud, your text messages and attachments no longer upload automatically, but they save in your next iCloud Backup and download in the background when you restore. Stay connected to Wi-Fi until the process finishes. The time it takes to restore depends on the size of your backup and the speed of your Wi-Fi.
Sometimes, if you restore a device from a backup of another kind of device, your Messages and Voice Memos won’t restore. For example, if you use an iPad backup to restore an iPhone, your Messages and Voice Memos may not appear on the iPhone.
If your information is still missing after you restore, you can try to restore from a different backup in iCloud or on your computer. Always back up your current data on your computer before you try to restore from iCloud Backup.
Have a great day!