WiFi assist actually does the opposite of what the OP wants. WiFi assist uses cellular data when in a weak wifi situation. So, you want to turn it off instead of on if you do not want cellular use while on wifi.
I can only assume that the phone occasionally loses WiFi signal and hence reverts to data. Do you occasionally reboot your modem, or walk away from its range? Or maybe your router has "channel optimisation" set, or whatever it may be called. This causes routers to monitor for channel clash and switch channels whenever it feels like. I always disable that option.
There is a bug in iOS 13 (all versions) whereby FaceTime Audio will occasionally switch to mobile data during a call if the person calling has a bad data connection. It's weird. Not sure it affects many people, but it could be the case. Which apps are showing as using mobile data when you check?