rustdoc: Index crates progressively (#13011)

This PR updates the rustdoc indexing to be more progressive.

Rather than waiting until we've crawled the entire crate to begin
writing to the database, we instead start writing the docs as we go.

This makes it so you can start getting completions while the indexing is
still running.

Release Notes:

- N/A

crates/rustdoc/src/rustdoc.rs

@@ -1,8 +1,9 @@
-pub mod crawler;
+mod indexer;
 mod item;
 mod store;
 mod to_markdown;
 
+pub use crate::indexer::{DocsDotRsProvider, LocalProvider, RustdocSource};
 pub use crate::item::*;
 pub use crate::store::*;
 pub use crate::to_markdown::convert_rustdoc_to_markdown;