rustdoc: Automatically index crates (#13014)

This PR removes the need to use `/rustdoc --index <CRATE_NAME>` and
instead indexes the crates once they are referenced.

As soon as the first `:` is added after the crate name, the indexing
will kick off in the background and update the index as it goes.

Release Notes:

- N/A

crates/rustdoc/src/indexer.rs

@@ -56,8 +56,6 @@ impl RustdocProvider for LocalProvider {
             local_cargo_doc_path.push("index.html");
         }
 
-        println!("Fetching {}", local_cargo_doc_path.display());
-
         let Ok(contents) = self.fs.load(&local_cargo_doc_path).await else {
             return Ok(None);
         };
@@ -91,8 +89,6 @@ impl RustdocProvider for DocsDotRsProvider {
                 .unwrap_or_default()
         );
 
-        println!("Fetching {}", &format!("https://docs.rs/{path}"));
-
         let mut response = self
             .http_client
             .get(
@@ -165,8 +161,6 @@ impl RustdocIndexer {
         while let Some(item_with_history) = items_to_visit.pop_front() {
             let item = &item_with_history.item;
 
-            println!("Visiting {:?} {:?} {}", &item.kind, &item.path, &item.name);
-
             let Some(result) = self
                 .provider
                 .fetch_page(&crate_name, Some(&item))