Laeral Silverhand really can attack with her hair. (Magic is probably involved.)
Chapter 1 of Death Masks demonstrates an example
For some very clear evidence that Laeral Silverhand can use her hair to attack people, see Ed Greenwood's novel set in Waterdeep, Death Masks. The official product page includes a link to a PDF of the "sample" first chapter, "A Nice Night for Murder". It includes several mentions of her hair.
First, Mirt "the Moneylender" and Elminster Aumar arrive at Mirt's former home, which has apparently been given by the Lords of Waterdeep to Laeral Silverhand in his absence (of over a century). They discover 6 assassins trying to kill Laeral, who is horizontally hovering in midair (p. 8-9; bold for emphasis mine):
Floating in midair at about head level for a man taller than Mirt was a sleeping woman, spread-eagled and horizontal and oblivious to all intruders. Her silver hair, the tresses long enough to reach to her ankles if she’d been standing upright, was spread out around her in a lazily restless cloud, almost a sphere of moving silver strands, and she glowed. [...[ Her bare feet were toward Mirt and Elminster as she floated on her back, her tresses drifting around her.
However, the assassins' crossbow bolts ("quarrels") and even a thrown dagger don't seem to reach her:
Mirt’s shout of warning came out as silence, but even as he barked it, those quarrels were slowing in midair, coming to a halt as Laeral’s hair drifted and swirled unconcerned around them.
The 5 assassins using crossbows charge in to try and stab Laeral, but find themselves foiled... by her hair:
Yet a running man, no matter how strong, swift, and agile, can make little headway if snatched off his feet and ensnared by hair as swift as a striking snake and as strong as a swooping dragon. Hair that could strangle and suffocate with ease, but instead merely pinions, ensnaring wrists and ankles and tugging so powerfully that the five owners of those captured limbs were bent over backward in midair, curled up into helpless arcs, like bent and straining longbows.
(The last assassin, who threw the dagger, tries to run away, but Mirt trips him and knocks him out.)
Laeral then opens her eyes. She tells Mirt and Elminster that she was "in reverie" (communing with the Weave), not asleep, and that "None of Mystra’s daughters ever need to sleep." She also praises Mirt on the defensive magic of the house (which may be what prevented ranged attacks from hitting her, given that her hair wasn't moving to stop them). Laeral then manipulates the Weave (without casting a spell) in order to directly probe their minds, but it causes her great pain (because Mystra wanted to disincentivize such a risky act that endangered the minds of both prober and target).
Lore and the statblock itself suggest that something magical is happening
Anyway, the above quotes make it clear that Laeral Silverhand's hair really is, essentially, able to attack and grab people. This is likely because she is one of the Seven Sisters, immortal daughters of the goddess Mystra that were her "Chosen"; this blessing grants them access to unprecedented magical power. While being a Chosen of Mystra is not known to be specifically connected to magic hair, her status as a Chosen and her own magical talents may have something to do with it.
Going back to Laeral Silverhand's statblock (Waterdeep: Dragon Heist, p. 207), we can see the following entries under "Actions":
Multiattack. Laeral makes three attacks with her silver hair and flame tongue longsword, in any combination. She can cast one of her cantrips or 1st-level spells before or after making these attacks.
Silver Hair. Melee Weapon Attack: +11 to hit, reach 5 ft., one target. Hit: 7 (2d6) force damage, and the target must succeed on a DC 19 Constitution saving throw or be paralyzed for 1 minute. The target can repeat the saving throw at the end of each of its turns, ending the effect on itself on a success.
Laeral is clearly very capable; she can make up to 3 attacks in a turn with her hair (and cast a cantrip or 1st-level spell on the same turn on top of that). In addition, it's worth noting that her silver hair, if it hits, does force damage, and has a high chance of paralyzing the target.
According to the description of damage types in the rules:
Force. Force is pure magical energy focused into a damaging form. Most effects that deal force damage are spells, including magic missile and spiritual weapon.
From this, it's clear that Laeral's hair is not just physically slapping enemies around. Rather, Laeral is able to channel magical energy through her hair to hurt a target she hits with it.