Similar to Jersey, Wisconsin's personality divides roughly into two stages, WWII and 1980s reactivation.
Young Wisconsin is very attentive and eager. As the third Iowa-class (yes THIRD. She was launched third and commissioned third, don't just assume off her hull number, she'll fight you on that) she's already late for the biggest war her county has known. So she wants to do everything she can to help, it's her motto after all "Forward." Despite the barn door tests that hurt her rudders, she's still in the pacific and joining her older sisters before Missouri even leaves California.
Her first days on the frontline goes great, full effect from her fleet's planes and she gets to learn from Iowa herself while Jersey commands the fleet. Just as she's learning the taste of war however, disaster strikes. Nine days after Wisconsin arrives, typhoon Cobra hits. Wisconsin handles it fine, but she learns quickly htta the weather is not her friend. Not only are three destroyers sunk, but Iowa is damaged and has to leave. Now she's stuck with a Jersey who's pining after her admiral, and she learns that she's not as important. But Wisky's a working battleship so she does her job, shoot the ground and feed the kids, even if the keep mistaking her for being last.
Even though she's late to the signing of the surrender, she's not the last even then. NJ is still returning from yard time.
Her first chance at decommissioning doesn't last long, she's quickly reawakened and sent to shoot more ground and feed more kids. But for once however, she's a flagship, since battleships are only really needed one at a time now and the admirals like her for some reason.
Her collision with Eaton teaches her that weather can cause worse things than sinking. She maintains an ever present nagging in that back of her mind from that point on. "Never get too close to a destroyer." Mentioning her new bow usually causes her to lock up though.
By the time the 1980s roll around she's mellowed out. Though she thought she was going to be scrapped the first time they came for her again. After all, it had been four years since she'd seen Iowa, or even heard of their other sisters. But she cares less about being the last now, claiming that they mean the last battleship from service, and though she doesn't like to think about Kentucky's bow, she justifies it by claiming it as a memory of a stillborn sister.
Though she's still wary around the new destroyers, her duties themselves haven't changed, shoot the ground and feed the kids. It's not until her active service is almost over that she finally gets to claim an achievement of her own, dubious that it is. She's the first to be surrendered to by UAV.
So projecting these events with what we've seen in story already lead me to think is that Wisconsin's personality would be very unenthusiastic. She'll do her job and do it properly, but she's not sure that she should be the one doing it. Because she knows who the Iowas are; The Face, The Fighter, The Famous, and The Forgotten. It hasn't changed for her; she's still the last battleship, the last choice, the last chance, the last one you could want. In her mind she's only on patrol because no one else can. Iowa's short a turret, Jersey's sunk and now on the west coast somehow, and Missouri is in the far more important Pearl; so important that Wisconsin had to give up boilers to ensure the good battleship is in the best of shape. So Wisconsin just plods along trying to find enjoyment in whatever escape she can, like a cartoon that depicts the ideal of a battleship. A ship that gets to fight other ships. A ship that was not forgotten even after she sunk. A ship that is the pride of her nation despite what she could never do. Not a leftover, half cannibalized ship who is only useful because she can remember some old radar patterns that showed up on her sister's radar.
That's my interpretation at least. Probably wrong, but I see her as the ship that did everything she was asked to but that no one remembers, which would be fine if she wasn't an Iowa class battleship.
