From what I gather from that, is it’s discussing how both 私は行く and 私が行く are on a very literal basis stating the same claim. However when you read them there is a clear difference, obviously this statement is intended to a Japanese child who would get the difference but not know why necessarily, and I suppose I am not at such a low level that I cant get that too, I do sort of. So it seems 私は行く is not just about what I am doing but innately that I am doing it, regardless of whatever others are doing (Well I mean, I’m going, I don’t know about anyone else, but me, I am." But 私が行く is more just a statement of what will occur, I will in fact be going. It emphasizes the fact that I am going as opposed to others around me.
What I find interesting is that it stated, 私は行く that you can interpret this as emphasizing the 行く when I would have though it emphasizes you, compared to others. But instead it emphasizes your action of going, compared to the action/inaction of others?
I would have thought its
私は行く - I am going (compared to others who aren’t)
私が行く - I am the one who is going (no one else is)
But it seems more like は is saying, my action is what is different, its not about me, its about the action of いく being different from other actions around me. and が is about it being ME who is doing the action, I suppose this lends credence to the は emphasizes what’s after, が what came before.
I’ll also be honest I don’t entirely understand even now how は is an adverbial particle, as my understanding of an adverb is it is supposed to describe how the verb is taking place or provide further detail to it, but I don’t think that makes much sense here as plenty of sentences lack a verb in general, but I guess you can say だ is である and stuff like that? And even so I fail to really see how the は is affecting the verb even if there is one in a way similar to はっきり or something. The case marking particles make a lot of sense, adverbial particle は makes little sense to me.
The resource you provided is super helpful, and I will definitely be saving it, thank you a ton for helping me out.