I wouldn't say she 'gains' powers from the marriage itself, more that her position as queen formalizes a set of inherent divine authorities she already kind of had. Her sphere—marriage, childbirth, women, the household—is intrinsically linked to her union with Zeus. It's less about unlocking new abilities and more about her role granting her the political and divine right to enforce those domains. The power to bless or curse marriages, to influence the outcomes of pregnancies, to shape the legitimacy of royal lineages, all that stems from her queenship.
Her infamous wrath against Zeus's lovers and their children is a brutal demonstration of that power. She can't overthrow Zeus, so she enforces the sanctity of her marriage by punishing everyone else, often with terrifying creativity. Turning Leto into a wandering outcast during her pregnancy, driving Heracles mad, orchestrating the long torment of Io—these aren't just petty jealousies; they're assertions of her divine jurisdiction. She's the guardian of a social order, and her power is the power to uphold it, violently if necessary.
So she doesn't get a lightning bolt upgrade. She gets the throne, the scepter, and the unquestionable right to make life miserable for anyone who threatens the institution she embodies. In a way, that's scarier than a thunderstorm.