HTTP endpoints should use structs from the API package and do full diffs in unit tests

Right now we often render internal RPC structures. If we use the API structures we will be better dogfooding those, and we will be more free to change the internal RPC representations without breaking the external interface.

As part of this process we should update the unit tests to do full struct diffs of expected values and not just compare some fields. This will also make us more robust to detect API breakage.