I disagree that the lack of a hard answer to the Fermi Paradox necessarily indicates that any technologically advanced civilization must invariably end up destroying itself. There are a variety of potential explanations that could explain our apparent solitude, of which a technological great filter is but one. For example, our universe is quite young, both in terms of how long a universe lives before its heat death and in terms of how long a universe continues producing stars capable of sustaining life. With this in mind, it’s entirely possible that we are simply the first to achieve sentience in our galaxy (as intergalactic travel is an unlikely prospect), especially if there is some particularly difficult evolutionary hurdle that we have already passed. Alternatively, it may be that communication methods detectable by us (such as radio emissions) are methods used only by technologically primitive spacefaring species, and so it could be that there is only a short window of time during which a species is visible to observers outside the system. And those are just two of a myriad of potential solutions to the paradox.
Space is vast, and the fact that we haven’t found anyone else yet should not be taken as proof nobody is out there. That’s like scooping a cup of water out of the ocean and declaring there are no fish in the ocean on the basis of that cupful of water alone. Looking more toward earth, I also want to note that humanity is a tenacious bunch. We have survived ice ages and super volcano eruptions in our past, climate extremes that mimic what could be produced by nuclear war. Undoubtedly, many of the outlined scenarios would be unpleasant and lead to an unacceptable loss of both human and non human life, but I find it unlikely that humanity wouldn’t cling on. Even if 99.99% of humanity died, that still leaves 800,000 people alive, and I doubt it would take more than 1000 years before we were back on our feet.