We are buying an electric mountain bike, a Specialized Turbo Levo SL, for my wife. It's a men's bike, and I see, for example, the SCOTT Contessa differs from men's models by having a women's seat, and narrower steering handlebars. Does it make sense to buy separate a women's seat for 1-3h, 3x/week rides? Do they differ much from men's seats?
What matters is that the saddle is comfortable for the rider given the rides they're doing.
There are obvious differences between male and female anatomy, which aren't to be neglected (here's some in-depth further reading, though the focus is on long road rides). This can lead to a need for different structure towards the front of the saddle in particular. This is most true if riding in aggressive (tucked) positions, so road racing, time trials etc.
We can't make any assumptions about how sit-bone width relates to hip/pelvis width or sex, and in a more upright position the sit-bones, which always bear most of the weight, are hopefully the only parts experiencing real pressure.
In technical mountain biking, you're not on the saddle much anyway, so it matters still less. Still, the longer end of this, if spent on the sort of trails where you'd sit down, can be really rather uncomfortable.
You don't say how much cycling she's done. If she's coming from very little, some initial discomfort may be expected - try gel-padded shorts/tights and anti friction chamois cream at first. New riders change quite a bit around the weight-bearing parts, and may even lose some fat, i.e. change shape, so rushing into a new saddle may not be a good idea.
My suggestion is that she starts with the stock saddle. It may be absolutely fine. If she's experiencing discomfort, especially numbness or obviously pressure-related discomfort that isn't improved by padded shorts and chamois cream, then it's time to look for a new saddle. It would be sensible at that stage to consider women's saddles, though not exclusively.
Firstly, I believe that Specialized have done away with men's and women's models of bike. When you look at the website the women's models are gone. So the saddle may or may not be a men's fit, just some kind of average for their main demographic (though that is probably men).
Secondly, in either case it wouldn't make sense to throw out the supplied saddle without putting it to the test, to just put on an untested women's-branded saddle. Either saddle could be perfect, or could be uncomfortable, but that isn't predicted well by gender. For all of us, some amount of trial and error is required to find the right saddle on the right bike, for the kind of riding we do. Some shops have tester saddles to avoid this being too expensive an undertaking.
You've discovered, by asking the question, that some manufacturers continue to offer female specific models with different contact points, while others simply have one line of 'unisex' bikes, because we're all so different and the gender line is so blurry for cycle requirements. Whatever gender, we can tailor the bike to suit us as an individual, whether or not they did some guesswork in the factory already.