Apparently I managed to activate it by using the Raiffeisen Twint application to pay. In the settings, it’s written that NFC is activated but I didn’t have the time to test if it realy works yet.
However, as the OP noticed, it doesn’t. There is a slider in the settings to turn on NFC, but it remains grayed out after you do this. I rarely use NFC, but sometimes you really need it, and it is embarrassing that their web site is not accurate about what they sell you.