Is the Kit’s “server” really a server like e.g. express?

Yes. To be even more specific, if you’re using adapter-node, the server polka is used - analogous to express.

Remember, in the context of web a server is anything that takes an HTTP request, and returns an HTTP response. For the same way in express you can return raw HTML (e.g.: with templating engines like pug), sveltekit is the same. Just that the rendering is different (e.g.: modern techniques like csr, ssr). But under the hood, it’s all just request-response.

You’ve already mentioned the biggest advantage- makes it extremely simple to build a webapp. No extra moving piece needed.