=I personally don't view analytical skill and stoicism as exclusively masculine virtues=
Womanly virtues are often associated with intuitive wisdom (which in my opinion can't be cleanly divorced from analysis) and effortless beauty. Women weren't allowed to write or play music for awhile because these were seen as "too passionate for a lady." These are, arguably, the same underlying virtues but expressed in different coats.
That said, I agree that the nature of Batman's stoicism and analytical ability are heavily masculine. His stoicism comes from brooding, wanting to avoid vulnerability, and his analysis tends to be aggressive and destructive.
I'd contrast this with a character like Supergirl. She's shown to not just rail against crime, but to take the time out of her day to go save kittens from trees, save children from burning buildings, talk people down with compassion, and so on. The thoughtfulness of Supergirl tends to be more feminine than the analysis of Batman.
=Are there examples of uniquely feminine expressions of these traits in pop culture?=
I think the superhero genre specifically, and its general appeal to action and shows of physical prowess, is probably the wrong place to be looking for feminine role models. It's easier to find in something like the Disney princesses, even though I'm aware of the common feminist critiques of the Disney princesses.
However, I don't personally feel like they tend to be any more toxic than most male role models, even if that toxicity shows itself in different ways. While Batman runs from his feelings and treats conflict too aggressively, for instance, Snow White doesn't really choose to strive towards any goals and treats conflict too passively.
It's worth noting that some feminine values do fall into pop culture through superhero films, though. The first Sam Raimi Spider-Man movie has themes of family and hospitality and, like Supergirl, Spider-Man is shown being more thoughtful with his powers by doing things like saving kittens from trees in a way that's portrayed as unironically heroic.