Swisscom knows nothing, the traffic - including DNS - would go to NordVPN. Depending on how NordVPN is configured, they will know everything about you but may not retain it.
If you want to hide your activity from Swisscom for free, take DNS at 1.1.1.1 and let HTTPS do the rest, they will likely have no clue what you are surfing to (best case is that they may know the site depending on certain circumstances, if you want to know more as ChatGPT to explain it to you)
Yes the Website you are visiting sees you "are" NordVPN (instead of you own provider adress) and you provider like Swisscom sees you are visiting NordVPN instead of the real site. NordVPN say they don't log where you are going and have a pretty good reputation. Also between you and Nord, the data is encrypted so it shouldn't be easy to look at what you are transmitting. Overall the only issue I have is that some sites don't like that you come from a VPN provider. (not many, but I had trouble logging on to post.ch and watching some SRG shows looks locked, probably due to rights) it's quite easy to switch off the VPN temporarily in that case.