[Cached Navs] Unify with prefetching implementation
When Partial Prefetching is enabled, every navigation response can be written
into the cache: either the entire response is cachable, or it contains an
embedded inner response that is cacheable. Conceptually it's as if each
navigation is accompanied by a corresponding prefetch, and both requests are
returned in the same response.
This unifies the implementation used to write the response (whether it comes
from a navigation or a prefetch) into the client cache.
