Hi Klaus1- I understand you're having difficulty setting up 2FA and the verification isn't appearing
You can find out information on how 2FA works here Two-factor authentication for Apple ID – Apple Support
There should be an option for "Did not receive code" have you tried setting that up?
Normally you should get a notification on your device which says someone is trying to log in to your Apple ID with their location, you click Okay to generate a code which is 6 digits and you can type it in, especially on a new-device or IP address.
Are you getting any pop-up at all ?
Do you have more than one Apple ID and are you trying to log into a different one?