Web component: handle async operations with built in Lit Task

[agjohnson]

In #300 I manually handled an async web request to our API, but I did almost use the Lit Task API to handle all of the async and error handling. I decided to put this off for a bit, while we are still figuring out web components here.

Maybe this is more refactor level work, or we might just take on the dependency early if we feel we'll definitely switch.

This list will grow if we continue to manually implement async task handling in Lit elements, but for now, the places where this pattern could be applied are:

• Notificaiton elements