I haven't read Agamben's book that you're discussing here.
It is true that isolation measures—lockdowns, remote work, etc.—are easier for those who have physically comfortable housing (especially with internet connections) and stable relationships. Many other people's jobs, though, require them to leave the house. So, indeed, the "technical calculation" of social distancing doesn't include or serve everyone equitably, and that is something that everyone should keep discussing.
But I don't really agree with the rejection of the idea that "the right to health has become an obligation to health" because I don't believe that this formulation even applies well to coronavirus. The difference is in discussing non-contagious and contagious diseases. If I want to live on a fast-food diet until my internal organs caved in, arguably that would be my own choice; I should have the right to healthier food options, but not necessarily the obligation to avail myself of them. My diet does not impact others' health. Coronavirus, by contrast, is a contagious respiratory disease. In minimizing the frequency with which I leave the house and contact other people, I am not only protecting myself, but more significantly I am protecting them. I try not to go out and breathe on other people, and the reason is that they have a right to health and therefore I have an obligation to help them maintain their health. To entirely rephrase, then: "[Other people's] right to health has become an obligation [for me] to [not actively negatively impact their] health." That formulation is generally true, it seems to me, and I do not have an ethical argument with it. It's impossible to consider contagious diseases solely as a matter of individual liberty, because they are shared, often with people who through no fault of their own are especially vulnerable to the contagion (because they are old or immunocompromised) or more likely to be exposed to it (because they are poor or they provide direct care for children). So everyone needs to avoid the virus, even if they feel no obligation to maintain their own health, so that they don't transmit it to others.