The correct syntax would be this:
set my_Col = my_col + 'new text'
where id = 123It has no "SELECT", so there is no roundtrip.
If there is nothing in my_col (i.e., if it is null), for it to work correctly, you also need to do one more thing, see below:
set my_Col = COALESCE(my_col,'') + 'new text'
where id = 123