Use new Storage endpoint model for deviceId

[jan-ivar]

From #674 (comment):

Can we refer to https://storage.spec.whatwg.org/ directly then?

We should, but it looks like doing so is blocked on whatwg/storage#18, so I think we should ... open an issue to come back to it.

[annevk]

We have a model now, but no API has been updated to make use of it so far (tracked in the issue linked above): https://storage.spec.whatwg.org/#model.