Hi NicoDRix,
Is your iPhone a managed iPhone from an employer or school? If so, then the Quick Start method is not for you. This is mentioned oil the article viewed before posting your question:
If your new device is enrolled in Apple School Manager or Apple Business Manager, you can't use Quick Start to transfer data from your current device.
If this is not the case, and since it looks like you've tried a few times, the next best thing to do is to use one of the other methods to set up your new iPhone.
Transfer data from your previous iOS or iPadOS device to your new iPhone or iPad - Apple Support
• Use an iCloud backup: Use iCloud to transfer data from your previous iOS or iPadOS device to your new iPhone, iPad, or iPod touch - Apple Support
• Use a Mac or computer backup: Use the Finder or iTunes to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support
If your new iPhone has some data already on it from the failed Quick Start method, you'll want to erase, so you can start over with a "clean" iPhone.
How to factory reset your iPhone, iPad, or iPod touch - Apple Support
1. Tap Settings > General > Transfer or Reset [Device]
Then tap Erase All Content and Settings.
2. If asked, enter your passcode or Apple ID password
Then confirm that you want to erase your device. Forgot your passcode or Apple ID password?
3. Wait for your device to erase
Depending on your device, it can take a few minutes to completely erase your data.
If you need further assistance, we'd advise to contact Apple Support, so they can work with you to get your new iPhone set up.
Apple Support
Take care!