The Kli Yakar on 3:1 writes (courtesy of sefaria):
There is a big question in this matter: If the woman added the command of "do not touch" by herself; behold, she knew the truth that God did not command about the touching. And if so, how was the woman seduced by these empty words, saying that in the same way as there is no death penalty from touching, so too is there no death penalty from eating? From a quick [survey], it appears that it can be explained that the woman did not hear the commandment from the mouth of the Mighty One, but rather from the mouth of her husband. And that is [the meaning of] what is written (Genesis 2:16), "And the Lord God commanded to (or about) the man, saying." What is [the meaning of] "saying?" Rather that he should tell his wife that this eating is dangerous. As it is for this reason that it is stated, "about" (al) and not "to" (al), meaning, regarding, that he not bring himself into danger. And the man saw in his [own] intellect to make a fence and to add upon the command; to forbid even touching to his wife, so that she should not come to eating. And Chava reasoned that everything he said to her was from the Mighty One.