I've been meaning to cancel online for two years. Went on the web site tonight and spent 30 minutes trying to turn this off. The cancel link takes me to a page with two sections, one where I can apparently buy vouchers (whatever they are) and the other just says I have a subscription. No option to turn off auto renewal. Talk about dark patterns. Any suggestions?
Edit: OK, whew. Took me two hours but I finally got it. Had to do it on the eShop on the Switch, which I didn't want to do because I knew I'd have to put in my new WiFi password and then run updates before it'd let me do anything.
The part where it says included in a family membership is the information you missed. Whichever nintendo account you are signed in on isn't the account that manages the family subscription you are in.
I had a similar experience once before so hopefully it's the same. Try to see if you can remove a family member? If that works then I'm not sure.