refactor(docs): adapt client lib documentation with new api calls

Author: Clément Turmel

docs/website/root/manual/develop/nodes/mithril-client-library.md

@@ -327,21 +327,32 @@ async fn main() -> mithril_client::MithrilResult<()> {
         .download_unpack(
             &snapshot,
             &immutable_file_range,
-            target_directory,
+            &target_directory,
             download_unpack_options,
         )
         .await?;
 
+    let verified_digests = client
+        .cardano_database_v2()
+        .download_and_verify_digests(
+            &certificate,
+            &snapshot
+        )
+        .await?;
+
+    let allow_missing_immutables_files = false;
     let merkle_proof = client
         .cardano_database_v2()
-        .compute_merkle_proof(
+        .verify_cardano_database(
             &certificate,
             &snapshot,
             &immutable_file_range,
-            target_directory,
-        )
-        .await?;
-    merkle_proof.verify()?;
+            allow_missing_immutables_files,
+            &target_directory,
+            &verified_digest,
+        ),
+    )
+    .await?;
 
     let message = MessageBuilder::new()
         .compute_cardano_database_message(&certificate, &merkle_proof)