I think you may be right about the model .my TV is not totally supported on smart thing only some fiction work am using a Series 7 smart tv UE50
Yes functionality will depend on the model,see a general guide here https://www.samsung.com/uk/support/tv-audio-video/how-to-control-your-tv-from-mobile-smartthings-app...
There are also some other universal Remote Apps, a few detailed in this guide https://www.universalremotereviews.com/remote-apps-for-samsung-tvs/
I do not work for Samsung or make Samsung Products but provide independent advice and valuable contributions.
My Device- S21 Ultra 5G ( SM-998B/DS ) CSC= BTU , 12GB/256GB
One Ui 5.0,Android 13 .