[roll] Roll fuchsia [bedrock] Merge get_router_or_error and with_path

The get_router_or_error function looks special cased to a particular
dictionary layout. For example, the RoutingError is used if the path
didn't cross a router, but discarded if the path did cross a router,
where it delegates to with_path.

It turns out we can merge these two functions, if we add the error
parameter to with_path. The body of with_path can also be much simply
rewritten using the get_with_request helper. The resulting function is
called `lazy_get` in this CL.

This reveals a cyclic logic in extend_dict_with_dictionary. The
function grabs a member from the program_output_dict, transforms it, and
inserts the result back into program_output_dict. In order to break the
cycle, we introduce a program_output() router that avoids holding onto
the underlying dict forever. Following the same shape we can introduce
component_output() and remove the adhoc new_forwarding_router_to_child
helpers.

Original-Fixed: b/329912531
Original-Reviewed-on: https://fuchsia-review.googlesource.com/c/fuchsia/+/1018316
Original-Revision: 06cd36b8a15b09731908ec0f78fe683923f8a527
GitOrigin-RevId: 4f243bdabf4580f5fbf828b76bcdba971d82fefd
Change-Id: I2fdbe194e7c341a870f3dad4a31fa34822f89dbc