### Context
Components currently can't access `LiteElement` utility methods without
being rendered into the light DOM. This is an initial step towards
breaking out parts of `LiteElement` into composable units. (see
https://github.com/webrecorder/browsertrix-cloud/issues/1380)
### Changes
Moves `apiFetch` from `LiteElement` into a reactive controller. New
components should use `APIController` directly instead of extending
`LiteElement`. We'll also work to move existing uses of `LiteElement`
off of it with time.
### Manual testing
No visible changes, skim through the app to verify that that backend API
fetches work as expected.
