The Folly of Minding One’s Own Business

Rashi: "to act treacherously against G-d"
Scripture repeats the section of a thief who swears falsely and "acts treacherously against God by falsely denying to his fellow." (Lev. 5:21) It is repeated here because two new matters are introduced. The first is that it is written: "they shall confess," which teaches us that he [the thief] is not required to pay a fifth and [bring] a guilt [offering] when incriminated by two witnesses, until he admits to the deed himself, and the second [matter] is that what is stolen from a proselyte must be given to the kohanim.

Baal HaTurim: "That person they shall confess"
hints to the Talmudic teaching that anyone put to death by a court of law should confess at the time of execution.

Ramban: [This verse is] similar to [the verse]: "of any sins which mans commit against another man when he deals falsely with his neighbor that soul shall be guilty," for he seeks a trespass against G-d Himself, as he swears by His Name falsely and is thus guilty before Him as well. Now because his sin has already been mentioned, here it introduces the new point of robbing a convert, dealing with it briefly. He mentions "a man or woman" because since it is not usual for a woman to rob, we might think that perhaps Scripture does not make her liable to pay the extra 5th or bring a guilt offering when she confesses the sin like a man, therefore He stated here "a man or woman" to show that her liability is the same as the man.

Or HaHayyim: Inasmuch as the person has committed perjury, he has caused damage to his very soul. Note that the Torah did not write that the soul of the sinner is guilty, but it writesthat "the person is guilty." This is a reference to the collective soul of the Jewish people that has become tarnished by one of its members committing perjury.

Zohar Naso 122:
Happy is the person who merits the Torah, to follow and adhere to His ways. When a person follows the ways of the Torah, he draws upon himself a holy Supernal Spirit, as it says: "Until a spirit be poured upon us from on high." (Isaiah 32:15) When a person diverts his ways he draws upon himself a spirit from the Other Side, which is the unclean side. That defiled side awakens from the side of the hole of the great abyss, wherein lie the wicked spirits that originated in Cain which harm people and are called the world's destroyers.
Jethro was originally a priest to idols and he served that side. He drew upon himself a spirit of that side. Therefore he was also called the Kenite later, since he separated from Cain and adhered to G-d. Whoever bonds to G-d and performs the commandments of the Torah, it is as if he upholds the worlds, the world above and the world below. This was already explained, as is written: "And make them." (Lev. 26:3)
Anyone who transgresses the commandments of the Torah, he, as it were, makes a flaw above and impairs below, becomes flawed himself and impairs the whole universe. This is similar to the seafarers on a ship, when a fool among them stands up and wishes to punch a hole
Therefore, "when a man or a woman shall commit...that man ('adam')..." is "But they like Adam have transgressed the covenant." (Hosea 6:7) Adam transgressed one command in the Torah, and he caused death to himself and he caused to the universe a blemish above and a blemish below. That sin is still impending until G-d will restore the universe to its original state, when that flaw will disappear from the world. It is written: "He will destroy death for ever; and G-d the L-rd will wipe away tears from all faces..." (Isaiah 25:8) Therefore, "Shall commit any sin that Adam commit," connotes "Adam" the first man.
"To trespass against G-d," (Num. 5:6) because whoever abandons mercy and draws on judgment causes a flaw. Therefore, the Merciful One should redeem us from the wicked of this world and from their damages, as many righteous pass away because of them, on top of what they caused to happen above and below.