Strange, I may have been to quick on my conclusion. While sending and receiving SMS worked directly after enabling VoLTE, it stopped working some time afterwards. I noticed by chance that sending and receiving SMS was not working a few days later. I also noticed, that the phone switched from WiFi to mobile data when I tried to send a SMS, not sure if this is intended.
So for now, I have to go back to ‘not working’ and investigate further, what the issue seems to be. As I was at a different location when noticing that it wasn’t working, it is possible that the issue may be related to the mobile cell or signal strength (or 3G vs 4G connections).