Just to update and for anyone else interested in the future, it seems that IMS was already disabled for me but I was still getting SMSs.

From what I understand, IMS is for SMS (and voice) over 4G, and even when IMS is disabled, SMSs are still enabled and active over 3G.

I haven’t found anything on the internet about the possibilty of completely disabling SMS so I’m not sure it’s possible.