To what extent and in what ways does it change your understanding of Jane Austen’s fiction to read it alongside the writing of Mary Wollstonecraft? Does it make sense to think of Austen as a feminist or proto-feminist writer, or would you resist that description?

This is a great question that shows a sophisticated understanding of the kind of thinking behind Jane Austen's novels. In her Vindication of the Rights of Women, Mary Wollstonecraft argues that women are badly educated in ways that do a disservice to their husbands and children and hence to the larger society. She argues that women are taught to be childlike, frivolous husband catchers rather than rational human beings. She asserts that neglecting women's education and teaching them to focus on superficials such as dress and hair makes them unfit helpmeets for their husbands and mothers who cannot offer proper guidance to their children. At the time she was writing, Wollstonecraft, though considered a radical, did not envision women taking on careers outside of the home but did passionately argue that they should receive better educations to properly fulfill their duties within the home.
Jane Austen's novels show that women who are not raised with a rational education cause trouble for themselves and others. A case in point would be Lydia Bennet in Pride and Prejudice, who has been brought up to be an empty-headed flirt who cares about little beyond clothes and soldiers. She is utterly impulsive and has no attention span. Neither of her parents have done anything to educate her towards a better path. Almost inevitably, she heads for ruin as she runs with Wickham—only the best of good fortune saves her.
Likewise, Emma Woodhouse in Emma is also brought up indulgently and has not acquired the self-discipline needed for sustained and sober study. She instead indulges in match-making and other mischief-making that threatens to damage the lives of people around her, such as Harriet Smith.
You can find other examples of this in Austen's novels: think of what happens to Maria Bertram, for example.
I would call Austen a proto-feminist. She is not a modern feminist, but protested the confined lives of women in her day and time. She is very much in line with the thinking of Wollstonecraft. A person does not have to be a twenty-first-century feminist to be on a path that argues that women deserve more rights and options. Austen was a feminist for her time and place—not radically so, but quietly revealing her critique of how women are treated in her society.