One thing that I didn't understand from this article was how you use this deployment platform.

Can you tell Claude code for web to build and deploy a web app using it? If so, does that end up with a public URL somewhere? Does that deployment continue working after your Claude code for web session ends?

The way I interpret this is:

After some inactivity it goes into some dormant mode. Where it will only consume some storage. The next time someone tries to access this artifact it just restores a snapshot from last working state.

I guess the public url part is working similar to how OpenAI and their Sites are. E.g: their personally only available to you, until you change the sharing options.