Hey there brohleder,
Thanks for reaching out to the Apple Support Communities. To get started, did you by chance have your messages synced with iCloud, or did you restore your iPhone from a previous iCloud backup when setting up your new device?
If so, check out the details in the following resource that can help with this missing information: 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.
Let us know if that's able to help.
Have a great day!