Implement serialization of assistant conversations, including tool calls and attachments (#11577)

Release Notes:

- N/A

---------

Co-authored-by: Kyle <kylek@zed.dev>
Co-authored-by: Marshall <marshall@zed.dev>

crates/semantic_index/src/semantic_index.rs

@@ -450,7 +450,7 @@ pub struct WorktreeSearchResult {
     pub score: f32,
 }
 
-#[derive(Copy, Clone, Debug, Eq, PartialEq)]
+#[derive(Copy, Clone, Debug, Eq, PartialEq, Serialize, Deserialize)]
 pub enum Status {
     Idle,
     Loading,