Extraversion meaning low assertiveness in this case? To be anecdotal, my dad is an ISTP 8w9, and while not strict or active like a TJ (especially ExTJ), can get serious, aggressive, and assertive that quick. Like he gets often impatient and annoyed with my ESFP brother's silliness and nuttery. My father isn't a socialable (in a sense of a socialite), either, and would often watch television in his room just to be undisturbed; and he is only talkative with friends or family only and not so much with strangers.
I think ISTJs, INTJs, and ISTPs are the introverts that are most likely to be Eights, and that's because of Te's major correlation and Se's slight correlation (Ti slightly amplifies the correlation in ISTPs).
Not just assertiveness, though that is a part of it. Extraversion is a thing that blatantly exists, right? We see that some people just keep going and going and do stuff nonstop, socialize a lot and can't stop talking, enjoy their creature comforts and so on. The question is, why? Jung&co. theorized that it's where your energy is directed, inward or outward, some popular conceptions basically amount to do you get energy from solitude or company and such things. But what actually causes extraverted behaviors?
Fundamentally, humans - any creatures - need reasons, causes for acting the way they do. Any creature, on average, only takes action because the rewards seem to outweigh the costs, and the systems that gauge how profitable or enjoyable rewarding signals are differ naturally between people - give someone with a high reward sensitivity the same set of inputs as someone low in reward sensitivity, and one will see a world abundant in opportunity to be seized and joy from things acquired, while for the other the rewards seem lower, and thus the costs seem higher in comparison, and he will see more of the world as a drain or a drag, more trouble than it's worth. There will still be things that filled their heart with joy and they'd totally end up doing those things, but their sphere of concerns would inevitably be smaller than that of the reward sensitive person, all else being equal. This is just a simple consequence of both perceiving similar costs but one sees things as more rewarding than the other - what those specific things are is of course very personal, but a highly reward sensitive person's sphere of interests will be wider, on average, and they will exhibit more positive emotions since wanting things and liking things is what drives us to pursue rewards in the first place.
The above is the fundamental force behind Extraversion and the true definition of the trait. It highlights some things: It gives us a clue as to the lived experience of Extraversion and so-called introversion and shows how an "introverted Eight" or an "extraverted Five" are oxymoronic: The way a Five is said to experience the world is incompatible with high Extraversion and the way an Eight or any Assertive triad type is supposed to experience the world is incompatible with low Extraversion.
We see that Jung&co. were wrong: Turning Extraversion lower and lower doesn't actually turn from "wide, outward and shallow" to "narrow, inward-turned and deep", it just narrows the sphere of interest - an "introvert" isn't necessarily a deep or especially inward-turned person at all, their narrow sphere of interest can just as well be collecting Turtles episodes. The Jungian style contrast makes sense when you play with concepts and language, but doesn't actually work out as operating parameters for a physical creature and doesn't fit evidence - Extraversion-Introversion makes good sense linguistically, but Extraversion-Detachment or Engagement-Detachment is probably closer to reality.
We can also see that extraverts are by no means necessarily shallow and unintellectual - if anything, it's the opposite, as Extraversion has a positive correlation with both aspects of Openness/Intellect, the personality trait that's linked to a bohemian, artistic type of character and to intellectual engagement. (Fives and Fours are characterized by both low Extraversion and high Openness/Intellect)
We can also see that social anxiety is not a form of introversion - an emotionally stable introvert simply isn't interested in social interaction because it is unprofitable. Anxiety is an active form of negative emotion, not the lack of active positive emotion that characterizes low Extraversion. This accounts for the popular conception of "where you get energy" - socializing is more often a positive hedonic deal for a highly reward sensitive person, while for the introvert it's more often a cost, but it's distinctly different from anxiousness related to social things or personal depth.
Now, if we look at the kind of experience that'd characterize high Extraversion, we'd see that it'd mean seeing the world as full of worthwhile things to do - worthwhile enough to actually do, not just think yea those are great but I can't be arsed, lots of positive emotion - not just happiness but an excited drivenness, a hungry want, and so on. A lack of this is completely against the Eight profile, wouldn't you agree? Of course, even introverts will experience times when they feel everything is abundant, and find things they feel very driven to do or feel things to be so in certain environments, and extraverts will find things they just aren't interested in or find life overwhelming sometimes, but the dispositional tendencies to certain experiences have to make sense if we are to actually describe someone's
character overall, not just their reaction to some particular situation or circumstance.