I feel so lucky with my cat. Would never dream of scratching me. Loves belly rubs. Most affectionate one in my life. If I ever pet him the wrong way he lets me know by giving me the gentlest "bite" basically just touching his teeth to my hand. I don't deserve him.
There are a shitton of examples of house cats that went wild cats. They'd do okay in the current climate. Dogs most likely as well. But I doubt any of those 3 species would survive in a climate that kills humanity...
If we go extinct, this will be the world of rats and roaches.
I don't think they are at any risk of going extinct. They are considered hyper-predators and dangerously invasive species for a reason. They have been moved to environments they weren't meant to be in and thrived there to the detriment of everything else several times over. Sure it will kill some of them, but overall they will probably come out on top.