I do not have a problem with Chat in Samsung Messages either,cetainly ensure Rich communications is toggled on in Settings. According to this article it depends on your carrier activating the the advanced Messaging Services for the stock samsung App. However it is specifically referring to the U.S https://www.androidcentral.com/how-set-rcs-chat-samsung-phones
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 .