“When it’s obvious that men specifically are being addressed in the Qur’an, it’s almost always as a commandment, or a lesson, that goes counter to the popular practice of the time — like in your example. It’s trying to teach men lessons that apply to men specifically, in societies that are patriarchal.
So, the Qur’an referring often to to men is not something for men to be proud of, and is not reflective of a special spiritual place, because most of the time, it is pointing out our injustices and discrediting common practices by suggesting alternatives modes of behaviour from the norm.
The fact that the Qur’an does not have similar commandments for women is just an acknowledgement of the situation of the society: there are a lot of things the men are doing wrong, which the women are either victims of, or do not have a role to play in due to their marginalized status (in the society).
There is one place where the Qur’an addresses a group of women in a similar fashion as the many (often condemning) lessons it gives to men: the wives of the Prophet are addressed directly in 33:30, and 33:32.
Again, they are being addressed here directly because this is only applicable to them, and is also a nod to the fact that they have a newfound status of power and clout as the wives of the Prophet. They are therefore reminded of the gravity of their position as role models.
Note that the Qur’an brings to mind the gravity of the Prophet’s position in a similar manner in other places by pointing out how grievous his punishment would be if he sought to cheat Allah or the believers.
The creator himself, thus, addresses women *specifically* in the Qur’an, where it is relevant, and *men* specifically, where it is relevant. There is no “extra spiritual status” to be had from it.
Apart from those specific instances, the Qur’an speaks to a general audience of mankind: men and women (when it uses some derivative of the word insan), and sometimes even more broadly to human men, human women, and the jinn – an entirely different species (when it just says they, or you, in the neutral/masculine/plural).
It’s also worthwhile to note that the Qur’an makes evident that women have just as direct a connection to God as any man. Just as some men are remembered in history only because of the strength of their character, so too are some women remembered in history solely because of the strength of their character (for example, the Pharoah’s wife).
Most relevant to your questions however, just as how some men have had angels bear them messages from their creator, some women, (for example Maryam, the mother of Jesus) too had this exact same connection.
Moses’ mother, in her time of duty, just like any male prophet, received direct divine inspiration and comfort:
“So We revealed to Moses’ mother, ‘Suckle him, then, when thou fearest for him, cast him into the sea, and do not fear, neither sorrow, for We shall return him to thee, and shall appoint him one of the Envoys” Qur’an 28:7. A.J. Arberry’s translation.”