If she wants to open an art gallery and travel around looking at art, isn't that extremely...

Well women aren't viewed really well and the only way she'd be able to open one is if she's a man and the only way she can visit one without damaging her reputation is if she's a man bc women aren't allowed to do anything without men in this setting But if she's got a male alias she can do everything she wants and more, completely alone BC it's not hobbies for her, it's what she wants for her future, that's how she wants to live (by viewing art and help artists/open art galleries)

She can do all that as a married woman without hurting her rep at all. She can always buy them under her husband's name if she's using an alias anyways. Also if she just brings a knight or attendant, I doubt anyone will care, they were only commenting about her being alone. Is she going to disguise herself as a man every time she wants to look at art? If so, what's stopping her from doing that now, if it bothers her? It doesn't seem like it bothers her at all now, do why would it in the future? Also why would she care about her rep? She's already going to be known as a divorcee which seems way worse.

Also did you forget the ML's mother is the one wanting to buy the paintings and was probably planning on going by herself if she hasn't gotten sick? Doesn't that mean no one cares about women taking an interest in art?

The issue would be her ability to scout artists and run the overall gallery. Not only would male artists not take her seriously, as tying yourself to a woman would be considered tying yourself to a sinking ship and would therefore risk your art going down in value. If she got close to any of them, met frequently with any of them, had a favourite or if any of them took a liking to her, she would end up in scandal (especially since historically a large portion of sponsorships within the art community were romantic/sexual). Regardless of if there were male chaperones present or not (ex. Marilyn Monroe and JFK, there's no physical or concrete evidence of an affair, but because of rumours and people's interpretations of 1 Happy Birthday song, the duo was covered in scandal)

Furthermore, women's skills and hobbies weren't taken seriously outside of courting men. You could have an interest in art if it was used to catch a man's attention, but any more than that was considered trival and frivolous. Therefore, women's opinions weren't respected, and their expertise wouldn't be taken seriously unless they used their husband's name for everything. So, doing any sort of business involving the gallery would be extremely difficult. Not only is she limited rights-wise. But men would refuse to do business with her, refuse to work with her and for her, refuse to have their art displayed in her gallery and just avoid general association with her (and probably not even attend the gallery if it was owned by a woman). Unless her husband was directly involved, which would result in them going over her head to her husband with every decision (which at that point, why bother having a gallery). Her husband would need to have a large role in the business. Any business deals would need to be conducted through him, the scouting of artists would need to be done by him, and any art worth value would need to be under his name to collect and maintain value.

The reason the ML's mom can have the freedom and power she has is because of the men she is tied to. Her social status prior to and during her debut would be closely tied to her father, and everything she had and would do would be a reflection of his status. Who you can be friends with, possible marriage prospects, and what balls you could attend would be all determined by your father's status (moving between social classes was also super rare despite what most stories show, so that's why breeding often matters as most of the time it determined what class you could marry into).

After marriage, her identity would be tied to her husband, his status and what he allowed her to do (ie, managing the household, your influence in society, giving her allowance/land, allowing her to do sponsorships, etc (also women often were gifted territories to manage by their family when married)). This is the reason why we see the trope of women fighting over the same man and women only attacking the mistress during affairs in literature and history. Since a woman's status was tied to her husband, if he abandoned her, she would be left in financial and social ruin (women were basically forced to fight against each other for their livelihood).

Finally, a large part of marriage and your status of widow is directly tied to your ability to produce a son/heir. Women would get more rights/control when they produced an heir because the power of the previous mother-in-law's rights would transfer to her (ie. the king's mom's duties would get transferred to the wife when she has an heir). The reason why widows can have freedom and status is because their sons loan their name to their mother (essentially, the mother would borrow and function under her son's name, status, and power, this is also why the horrible mother in laws are a thing because a wife is a threat to their status and power). Also, within the relationship of 'mother & son', the mother holds the authority role compared to 'father & daughter' and 'husband & wife' relationships, where the father and husband hold the authority figure roles over the woman. This is why, during that time, the role of widow had the most freedom for a woman (most sons wouldn't control their mother's freedom and bodily autonomy, unlike a father or husband). So, essentially, the mom in the story can do what she wants because of the social status she has cultivated and because her son gives her the power to do so. She's able to buy art because she's the mother of the duke. She is still going through her son's name and her relation to him. So, when the MC says she wants the privileges of a man, she wants the ability and freedom to own and do things without needing permission and having to go through a 3rd party for everything. She also does not have full bodily autonomy, which is why, despite writing a contract and agreeing with the duke at the end of this chapter, we are reminded that he still needs to talk with the father and reach an agreement or the whole thing is null and void.