I think reading classical liberal authors like Locke, Hume, Mill, Bentham, Ricardo, Smith, Voltaire, and Montesquieu is the best way to understand. (And as an aside, I think absolutely everyone on Earth should read Kant, to understand anything that came after him, it is necessary without a shadow of a doubt, even to understand Marxism). But overall, starting with where these ideas came from is the ideal way in my mind.
Even if they are labor aristocracy, which the good majority aren’t, that doesn’t make them not working class. Working class refers to your position in relation to the means of production
The vast majority of people who are in higher education and students are working class. The idea that they aren’t isn’t a Marxist view of classes.
Most community colleges offer Associates Degrees, which are normally two years and below a Bachelor’s degree. Often it can also make it easier to get a Bachelor’s later on if you wish to.
You can get good scholarships to universities. The idea that everyone had debt isn’t totally true. Many people are able to walk away with zero tuition for example with having scholarships which would make you not need debt if you also live at home.
That’s a problem sure, but that doesn’t make them not working class. A white collar worker has the same connection to the means of production as a blue collar does. The revolutionary potential and place within society. What I am saying boils down to two main critiques.
First off, it is important that we are clear in the differentiation of class, otherwise we risk diluting how class analysis actually underpins the way we analyze and view everything we ever see. I understand the idea that the class character is different, but the class relation is not.
Secondly, even if this is true, this is not a reason to not seek education. Without education, we would not have Marxist theory, nay, any writing at all. To understand the world around you, you must become educated on it in every way possible.