I don’t know, insects have been doing pretty well for a long time, and only one large group of insects that we know of has ever gone extinct, even during the absolutely horrific Permian-Triassic extinction event.
I know as humans our impulse is to “do something about it”, but I think insects are gonna be fine.
Insects may do fine, but individual species are another story.
For example through most of Los Angeles, if you see an ant it is probably an Argentine ant (Linepithema humile). Over my son's life, the variety of native ants to be found near me has visibly declined.
Sure insects in general will be "fine", but ecosystems will have to be rebuilt over time with the different dynamics.
Take bees/pollinators. Another species could evolve or otherwise step in to fill the gap, but it could well result in many other plant and animal species also going extinct in the process.
Similar scenario with climate change. The earth will continue to exist and there will continue to be weather. But that weather could be a lot more inhospitable to our very narrow definition of habitable.
Yes, I know global warming doesn't mean the end of the (human) world as many suspect and are skeptical about. Humans will find a way to survive in special habitats and in much smaller numbers. What's at stake is the current civilization. With civilization's collapse we're bound to repeat this progress to self-destruction cycle.
I know as humans our impulse is to “do something about it”, but I think insects are gonna be fine.