The provider-scoped engine handle, narrowed to the
registration capability (FamilyGraph). The factory is
expected to call graph.input(...) or graph.derived(...)
exactly once and return the resulting handle. Methods outside the
narrow surface (commit, hydrate, snapshot, subscribeCommits,
…) are intentionally unreachable from here — they are not the
factory's responsibility.
The keying identity passed to the hook.
The freshly-registered node handle.
Factory that produces (and registers, via
graph.input/graph.derived) a node for a givenkey.