I can imagine them climbing on top of cathedrals or tower apartment blocks and curling up on the roofs to soak in the sunlight while the buildings precariously creak under the cats' weight and eventually collapse. The giant cats unfazed move to the next cathedral ... that would be a very British giant cat apocalypse.
Why not both? I mean, the standard Skynet murder robots/nuclear apocalypse scenario is indeed boring. Skynet x AlphaFold solving protein folding and hitting us with molecular nanotech? Swarms of giant murder cats would be on the table.