Answer

The plain meaning of the verses deals with confession over a sacrifice, not confession over sins in general as part of repentance. In Sefer HaMitzvot, positive commandment 73, he himself raises this question and answers it:
And the 73rd commandment is that He commanded us to confess the sins and iniquities that we have committed before God, exalted be He, and to state them together with repentance. This is confession. Its form is that one says: “Please, Lord, I have sinned, I have acted wrongly, I have transgressed, and I did such-and-such.” He should elaborate and ask forgiveness in this vein according to his eloquence. Know that even those sins for which one is liable to bring one of the types of sacrifices mentioned above, where God, exalted be He, said that one who brings them receives atonement—even then, the sacrifice without confession is not sufficient. As He said, exalted be He: “Speak to the children of Israel: A man or a woman, when they commit any of the sins of man, to act treacherously against the Lord, and that soul shall be guilty; and they shall confess their sin that they committed.” And the language of the Mekhilta in explaining this verse is: Since it says, “and he shall confess that wherein he sinned,” he should confess the sin that he committed—over it, over the sin-offering while it still exists, not after it has been slaughtered. Does this imply only that an individual confesses for entering the Temple in impurity? For that verse—namely, “and he shall confess that wherein he sinned”—appears in Leviticus in the section dealing with one who defiles the Temple and its sacred things, and with the related cases we explained. And it says there in the Mekhilta that we learn from that verse only the obligation of confession for one who defiles the Temple. From where do you include all the other commandments? Scripture says: “Speak to the children of Israel… and they shall confess.” And from where do you include even those punishable by death or karet? It says “their sin.” “All their sins” includes prohibitions; “when they commit” includes positive commandments. And there it also says: “any of the sins of man” — matters between a person and his fellow, such as theft, robbery, and slander; “to act treacherously” includes one who swears falsely by the Name and one who curses; “and that soul shall be guilty” includes all those liable to death, that they too must confess. One might have thought this applies even to one executed on the basis of conspiring witnesses; therefore it says: “and that soul shall be guilty”—meaning, he is not obligated to confess if he knows he has no sin but false testimony was brought against him. Thus it has been explained to you that for all types of sins, great and small, even positive commandments, one is obligated to confess them. And because this command—“and they shall confess”—appears together with the obligation of sacrifice, one might have thought that confession alone is not an independent commandment but merely something ancillary to the sacrifice. Therefore they had to explain in the Mekhilta in this language: One might think that only when they bring a sacrifice do they confess; from where do we know that even when they do not bring one? Scripture says: “Speak to the children of Israel… and they shall confess.” And still this only implies confession in the Land; from where do we know it applies even in exile? Scripture says: “And they shall confess their iniquity and the iniquity of their fathers,” and so too Daniel says: “To You, O Lord, belongs righteousness, but to us shamefacedness.” Thus it has been explained to you from all that we have mentioned that confession is an independent commandment, and an obligation upon the sinner for whatever sin he committed, whether in the Land of Israel or outside it, whether he brought a sacrifice or did not bring a sacrifice—he is obligated to confess, as He said, exalted be He: “And they shall confess their sin that they committed.” And the language of the Sifra as well is: “And he shall confess” — this means verbal confession. The laws of this commandment have been explained in the last chapter of Yoma (86b, 87b).
As for the blessing, I do not know. Perhaps it is because it is disgraceful to recite a blessing in the context of sins. I came under an obligation to repent because I sinned, and there is nothing to bless over in that.