Support clear SessionStart source (#17073)

## Motivation

The `SessionStart` hook already receives `startup` and `resume` sources,
but sessions created from `/clear` previously looked like normal startup
sessions. This makes it impossible for hook authors to distinguish
between these with the matcher.

## Summary

- Add `InitialHistory::Cleared` so `/clear`-created sessions can be
distinguished from ordinary startup sessions.
- Add `SessionStartSource::Clear` and wire it through core, app-server
thread start params, and TUI clear-session flow.
- Update app-server protocol schemas, generated TypeScript, docs, and
related tests.


https://github.com/user-attachments/assets/9cae3cb4-41c7-4d06-b34f-966252442e5c

codex-rs/app-server-protocol/src/protocol/v2.rs

@@ -413,6 +413,14 @@ v2_enum_from_core!(
     }
 );
 
+#[derive(Serialize, Deserialize, Debug, Clone, Copy, PartialEq, Eq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(rename_all = "camelCase", export_to = "v2/")]
+pub enum ThreadStartSource {
+    Startup,
+    Clear,
+}
+
 #[derive(Serialize, Deserialize, Debug, Clone, PartialEq, Eq, JsonSchema, TS)]
 #[serde(rename_all = "camelCase")]
 #[ts(export_to = "v2/")]
@@ -2633,6 +2641,8 @@ pub struct ThreadStartParams {
     pub personality: Option<Personality>,
     #[ts(optional = nullable)]
     pub ephemeral: Option<bool>,
+    #[ts(optional = nullable)]
+    pub session_start_source: Option<ThreadStartSource>,
     #[experimental("thread/start.dynamicTools")]
     #[ts(optional = nullable)]
     pub dynamic_tools: Option<Vec<DynamicToolSpec>>,