About a year ago (i.e. in 2020) I read a book which was intended to be the first of a trilogy about a sneaky invasion by the inhabitants of one giant spire against another. The story is told from the point of view of the inhabitants of the spire that is invaded, and tells how they discover and partially fight the well trained army of the other. Each of the floors had different characteristics and different wealths. One floor had a port for incoming air ships, another was a floor for the benevolent royal family. There were different creatures as well as humans, including clans of sentient cats. These cats had their own ways of doing things. The heroine’s cat helps organise a defence of the invasion of spiders that are working with the human attackers. Each spire had its own (air)navy with heavy battleships and lighter, more nimble cruisers.
The inhabitants of the spires had no memory of who and when the spires were built. The spires were built of a very resistant and long lasting material. The inhabitants would alter the interior by building with wood and stone but they could not change or destroy the original.
I could not read the next in the series because at that time it had not yet been written. I made a mental note to look for the next but, in the last year, I forgot the name of the book and of its author.