Serverless is specifically a stateless paradigm, making testing easier than persistent paradigms.
> Framework adoption?
Generally we use our own frameworks - I do wish people knew there was more than serverless.com. AWS throw up https://arc.codes at re:Invent, which is what I'm using and I generally like it.
> Stability? Industry Skills? Proven Architectures...?
These are all excellent questions. GAE, the original serverless platform, was around 2010 (edit: looks like 2008 https://en.wikipedia.org/wiki/Serverless_computing). Serverless isn't much younger than say, node.js and Rust are. There are patterns (like sharding longer jobs, backgrounding and assuming async operations, keeping lambdas warm without being charged etc) that need more attention. Come ask me to speak at your conference!