We're having a rough time here because you're still not being charitable in your construction of the original author's meaning. This is a skill that takes time and practice, so I'm not surprised. It's also a skill that is subverted by a desire to "win" a conversation. This subversion generally takes the form of mistaking the goals of debate for the goals of conversation: Conversations are for "finding out," while debates are for "winning."
Let's try situating "anxiety" within the context of how Marx would have viewed it. That is, how would the term "anxiety" arise in a discussion of class dynamics in a capitalist system? (This was one of the main concerns of Marx's work.) In that context, it shouldn't take too long to see that the term "anxiety" is going to arise from discussions about exploitation. Namely, the means by which concentrated capital exploits labor is by threatening labor with explicit physical violence and the implicit violence of removing from sectors of the labor market the ability to sustain their livelihoods (in punishment for things like striking for wages or for raising grievances, among others).
This is different from the mood of "anxiety," I think you'll (eventually) agree. I mean, the flip side of the Hedonic treadmill is, of course, the "frog in the pot" syndrome. Setting aside the apocryphal origin of the idea, it is just the Hedonic treadmill in the other direction; We accommodate to unpleasant or undesirable circumstances when we have to. For example, there used to be an effective Bill of Rights in the United States. There isn't, now. Nobody seems especially down about this from moment to moment, not even people who were especially proud that those protections were in place to begin with. However, even if our collective heartbeats aren't elevated 100% of the time, I think there's still "anxiety" about this. Accommodating to this kind of anxiety doesn't make it go away. We just stop physiologically responding to the stimulus. We still know to not voice criticisms that might sound unpatriotic. We still know not to get too close to Muslims in our communities, for fear of state violence, no matter how sublimated or indirect that violence is. Those behaviors come from accommodating to and normalizing our lives in the face of anxiety.
That's the kind of distinction to which Marx and Marxist analysts are pointing when they talk about "anxiety." That's typically their meaning when they use the term. This is a perfectly ordinary way to use words, and the attempt to subvert it by equivocating on the meaning/definition dichotomy is a feature of folk intellectual pseudo-rhetoric. For example, you have done precisely this with my use of the word "extremity." Let me point out that, again as an example, that my hands and feet are my "extremities," but we don't put pictures of them on sports drinks in order to get people to think that they can adopt the cache of the thrill-seeking activities called "extreme sports." Similarly, in my reply to you, I was using another sense of "extremity" as a near synonym of the phrase "the degree of." My point was not that the anxiety was debilitating to everyday tasks, nor that it had the psychological immediacy of having a gun pointed to your head, nor anything like that. The point, charitably constructed, is that capitalistic systems, insofar as they prioritize the interests of concentrated capital over the livelihoods of the laboring classes, structurally use existential anxiety as a tool for manipulation. Whether or not you are or are not "particularly anxious" in your moment-to-moment emotional experience is entirely beside the point. Are you at a job? What is your motivation for being at that job? If you're asked to do something immoral in that job, won't your thinking on whether or not to obey be influenced by the potential loss of income if you disobey? See? Anxiety.
Maybe you can now see why it's frustrating to have you state that this is "an extraordinary claim." First, the Extraordinary Claim trope, as cemented in folk pseudo-intellectualism, frequently first has to do all this work to construe a perfectly ordinary claim, perfectly ordinary use of terms, as extraordinary, which you have done. Only then can it get to its real purpose, which is to create an imaginary "Burden of Proof," and then shift it to the other conversant, as if that conversant were an opponent. As such, it turns all subtle and involved conversation, all sophisticated power struggles that comprise real conversation, into cheap debates. It suspiciously does so in a way that always flatters the one who offers it. It's a classless debasement of the intellectual life. Second, this trope hides the distinction between definition and meaning so successfully that I'm not sure that, even after my responses to you so far, that you'll be able to usefully use the distinction.
I hope that it's beginning to become clear, though. A richer and more meaningful participation in matters of life and mind await you if you can figure it out.