The screen shot you show has nothing to do with your mobile data state, it's just giving you the SIM card status, which should be in an "always on" state since you do have phone service.
Also, unless you changed the defaults somehow, Samsung devices automatically stop using mobile data if they have a WiFi connection. You generally see the 4G (or whatever icon you might have) icon in the status bar disappear and the WiFi icon come up to replace it. Also, if WiFi calling is enabled, some devices will show a VoWiFi icon, but Samsung devices (or at least the ones I've dealt with) do not.