I managed to make it work with NFC on webauthn.io and IOS 15.2. The iphone is in a leather case. Do it as follows:

• Move your key at least 10-15 cm away from the iphone so that it does not pick up any signals. The iphone is a bit picky on that part, also with other NFC devices.
• Go to webauthn.io. Enter a username and click register
• Select in the Safari popup to use a security key
• Turn the key that the side without any writing is pointing towards the back of the iphone at the level of the notch (note this is the latest iPhone. Other iphones might have the NFC reader somehwhere else). The key must directly touch the iphone
• You should be asked for a PIN (you can configure a PIN before in Chrome)
• Enter the PIN
• You are registered
• Move away the key for 20 seconds from the iphone (ca 15-20 cm) to make sure that the iphone does not get confused
• Click login
• Move the key as described above to the back of the iphone and also have the touch sensor touched
• enter pin
• you can login

I repeated it a couple of times and it works. I have to admin it requires a bit of training, but afterward it works smoothly. I have similar issues with other NFC devices on the iPhone so I do not think it is Nitrokey-specific for now.

Troubleshooting:

• If it does not work then move the Nitrokey at last 15-20 cm aways for 15-20 seconds.
• Directly touch the case or the iphone with the key - it must be really close.
• Make sure to find the exact spot of the NFC reader of the iphone. For the newest iphones a good position seems to be directly behind the notch