Fast sync child trie support. (#9239)

* state machine proofs.

* initial implementation

* Remove todo.

* Extend test and fix import.

* fix no proof, with proof ko.

* fix start at logic.

* Restore response size.

* Rework comments.

* Add explicit ref

* Use compact proof.

* ref change

* elaborato on empty change set condition.

* KeyValueState renaming.

* Do not add two time child trie with same root to sync reply.

* rust format

* Fix merge.

* fix warnings and fmt

* fmt

* update protocol id to V2

substrate/client/api/src/backend.rs

@@ -42,7 +42,7 @@ use std::{
 	sync::Arc,
 };
 
-pub use sp_state_machine::Backend as StateBackend;
+pub use sp_state_machine::{Backend as StateBackend, KeyValueStates};
 use std::marker::PhantomData;
 
 /// Extracts the state backend type for the given backend.