As used today, a soothsayer is a person who can, or at least is alleged to be able to, forecast the future accurately.
This is not a new meaning, it has been in use for about three hundred years, but it is not in agreement with the original sense.
Sooth was, to start with, an exact synonym for truth, and a soothsayer was merely one who was truthful.
But charlatan fortunetellers have been with us a long time, and they are most anxious that their gullible patrons should believe in the truth of their predictions.
Hence it was quite to be expected that they should protest that they were saying sooth, i.e., “telling the truth.”
Sooth, today, lives only in this word and in forsooth (“in truth! certainly!”; chiefly ironically), except that it is sometimes used as a deliberate archaism.