We often see Hera punishing Zeus's children or the mothers because of her jealousy. But such is not the case with the hero Perseus or her mother. She isn't even mentioned trying to cause any harm to them (that I have thus read). Why is that? What doesn't Hera antagonize Perseus as she did Heracles, Leto, Io, Echo, Semele, Dionysus and many other?
Yes, she did know.
There are at least two ancient sources which make this explicit, the first being Nonnus' Dionysiaca, which places the reign of Perseus in Argolis during the time that Perseus' half-brother the wine-god Dionysus is concluding his epic tour of Greece. At the end of Dionysus' itinerary is the region of Argolis, one of whose major cities is Argos, partly ruled over by Perseus' relative Melampus.
Argos is famously known as a city dedicated to Hera. Centuries before Perseus and Dionysus were born Poseidon and Hera had contended strongly over who, between the two of them, should become the city's patron deity, and Perseus' ancestors had granted Hera this honour. In Dionysiaca 47, by the time that Dionysus comes with his campaign entourage to Argos, the notoriety of Hera's hatred of him is so widespread that the Argives are fearful of a reprisal from their goddess if they receive this enemy stepson of hers. The citizens therefore turn Dionysus' army away from their home, which then provokes a retaliation by Dionysus, who induces madness in the city's women so that they start to butcher their own children.
This in turn attracts Hera's attention, who swoops to the aid of her city by disguising herself as Melampus and, in this form, goading Perseus into defending Argos against Dionysus' attack. In the fight that ensues, Dionysus' new bride Ariadne gets turned to stone by Perseus, who achieves this by using the deadly head of the slain Gorgon Medusa. An enraged Dionysus is then ready to destroy the city as well as other parts of Argolis, threatening to annihilate the land's inhabitants, at which point another half-brother, the messenger-god Hermes, appears behind him and convinces him to cease fighting, explaining that Hera, who is involved in the battle, possesses the power to defeat him.
With Hermes' help, Dionysus and Perseus afterwards become friends while the real Melampus establishes the cult of Dionysus in Argolis. The wine-god then moves on from there to Thrace to conclude his adventures in the final book of the Dionysiaca.
~ from my Answer to another Question
In the speech used by the disguised Hera to stir Perseus up in defense against Dionysus, she references the conception of Perseus by his mother Danae, urging Perseus to:
remember the bronze vault which was Danae's chamber, where Rainy Zeus poured into her bosom a shower of bride-stealing gold—let not Danae, after that bed, after the wedding of gold, bend a slavish knee to that nobody Dionysus. Show that you have in you the true blood of Cronion [Zeus], show that you have in you the golden breed, proclaim the bed that received that snowstorm of heavenly riches... Why do you tremble before Dionysus, no offspring of the bed of Zeus?
The play Hercules Furens, by the Roman writer Seneca, opens with Juno (the Roman Hera) listing a number of her husband's indiscretions with other women and how different aspects of these illicit unions are celebrated across the sky itself in the form of constellations. In the case of the Gorgon-slaying hero, after his death, Zeus made him into the constellation Perseus. Juno refers to the women in her catalogue here as harlots, bearing a clearly much less flattering perspective than the one presented by Nonnus.
The first of our sources above is describing the last known adventure of Perseus before he settles down to family life and has quite a few kids. The second source describes a scene occurring a few generations after Perseus is dead. It is perhaps not impossible that Hera only learned of Perseus' paternity later in his lifetime. In Perseus's Dionysiaca cameo, Hera seems quite happy to have her Gorgon-slaying stepchild as a lord of her favoured urban location.
If Hera does in fact know from earlier on that Perseus is her stepson, my other guess is that she does not bother harassing him or his mother because they are not special favourites of Zeus in the same way the ones you mention in your Question are. Leto's twins, and Dionysus, and Heracles are perhaps the topmost favourite children of Zeus of all time (with the exception of the ancient horned god Zagreus). Perseus and his mother, on the other hand, receive no particular attention from Zeus that I am aware of.
When Perseus was born his grandfather Acrisius put him and his mother in a wooden chest which he cast into the sea in the hope of killing the newborn boy. This episode is the single direct interaction that I have found between Zeus and Perseus after the latter's conception and before the hero's being made into a constellation after his death. Hyginus tells us that Zeus caused the seaborne chest to be carried to the island of Seriphos, where Perseus grew up in obscurity, living together with his mother and the poor fisherman who found them when their box arrived upon his shore.
Whether Zeus simply cared so little for them or he was trying to hide them from Hera or Acrisius, we are not told. In at least one instance of Zeus siring his dozens of children he was such a deadbeat dad that one is left to wonder whether he was even aware this offspring existed. Some of his children are obscure enough for this to plausibly have been the case with them in general. There's also a handful of his children with whom Zeus shares a hostile relationship (one of these is killed by Zeus himself). Perhaps towards Perseus he was fairly indifferent for a good chunk of the hero's life. The Iliad, though, does have Zeus boasting to Hera, during the Trojan War (generations after Perseus' death), that his son Perseus was the "greatest of warriors".
Whatever Hera's reason for not persecuting Perseus and Danae is, she was certainly aware, at least by some point prior to Dionysus' Argos début, that Perseus was her stepson. Among Zeus' love affairs and illegitimate offspring, however, Perseus and Danae are not unique in remaining unmolested by the queen of the gods, neither is Perseus the only stepchild of hers with whom Hera found occasion to team up against a mutual opponent.