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/src/codex_message_processor.rs

@@ -2236,6 +2236,7 @@ impl CodexMessageProcessor {
             experimental_raw_events,
             personality,
             ephemeral,
+            session_start_source,
             persist_extended_history,
         } = params;
         let mut typesafe_overrides = self.build_thread_config_overrides(
@@ -2277,6 +2278,7 @@ impl CodexMessageProcessor {
                 config,
                 typesafe_overrides,
                 dynamic_tools,
+                session_start_source,
                 persist_extended_history,
                 service_name,
                 experimental_raw_events,
@@ -2352,6 +2354,7 @@ impl CodexMessageProcessor {
         config_overrides: Option<HashMap<String, serde_json::Value>>,
         typesafe_overrides: ConfigOverrides,
         dynamic_tools: Option<Vec<ApiDynamicToolSpec>>,
+        session_start_source: Option<codex_app_server_protocol::ThreadStartSource>,
         persist_extended_history: bool,
         service_name: Option<String>,
         experimental_raw_events: bool,
@@ -2475,6 +2478,12 @@ impl CodexMessageProcessor {
             .thread_manager
             .start_thread_with_tools_and_service_name(
                 config,
+                match session_start_source
+                    .unwrap_or(codex_app_server_protocol::ThreadStartSource::Startup)
+                {
+                    codex_app_server_protocol::ThreadStartSource::Startup => InitialHistory::New,
+                    codex_app_server_protocol::ThreadStartSource::Clear => InitialHistory::Cleared,
+                },
                 core_dynamic_tools,
                 persist_extended_history,
                 service_name,
@@ -4443,7 +4452,7 @@ impl CodexMessageProcessor {
                 thread.preview = preview_from_rollout_items(items);
                 Ok(thread)
             }
-            InitialHistory::New => Err(format!(
+            InitialHistory::New | InitialHistory::Cleared => Err(format!(
                 "failed to build resume response for thread {thread_id}: initial history missing"
             )),
         };
@@ -9114,7 +9123,7 @@ pub(crate) async fn read_rollout_items_from_rollout(
     path: &Path,
 ) -> std::io::Result<Vec<RolloutItem>> {
     let items = match RolloutRecorder::get_rollout_history(path).await? {
-        InitialHistory::New => Vec::new(),
+        InitialHistory::New | InitialHistory::Cleared => Vec::new(),
         InitialHistory::Forked(items) => items,
         InitialHistory::Resumed(resumed) => resumed.history,
     };