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/core/src/thread_manager.rs

@@ -474,6 +474,7 @@ impl ThreadManager {
     ) -> CodexResult<NewThread> {
         Box::pin(self.start_thread_with_tools_and_service_name(
             config,
+            InitialHistory::New,
             dynamic_tools,
             persist_extended_history,
             /*metrics_service_name*/ None,
@@ -485,6 +486,7 @@ impl ThreadManager {
     pub async fn start_thread_with_tools_and_service_name(
         &self,
         config: Config,
+        initial_history: InitialHistory,
         dynamic_tools: Vec<codex_protocol::dynamic_tools::DynamicToolSpec>,
         persist_extended_history: bool,
         metrics_service_name: Option<String>,
@@ -492,7 +494,7 @@ impl ThreadManager {
     ) -> CodexResult<NewThread> {
         Box::pin(self.state.spawn_thread(
             config,
-            InitialHistory::New,
+            initial_history,
             Arc::clone(&self.state.auth_manager),
             self.agent_control(),
             dynamic_tools,
@@ -668,6 +670,7 @@ impl ThreadManager {
             ForkSnapshot::Interrupted => {
                 let history = match history {
                     InitialHistory::New => InitialHistory::New,
+                    InitialHistory::Cleared => InitialHistory::Cleared,
                     InitialHistory::Forked(history) => InitialHistory::Forked(history),
                     InitialHistory::Resumed(resumed) => InitialHistory::Forked(resumed.history),
                 };
@@ -1070,7 +1073,7 @@ fn append_interrupted_boundary(history: InitialHistory, turn_id: Option<String>)
     }));
 
     match history {
-        InitialHistory::New => InitialHistory::Forked(vec![
+        InitialHistory::New | InitialHistory::Cleared => InitialHistory::Forked(vec![
             RolloutItem::ResponseItem(interrupted_turn_history_marker()),
             aborted_event,
         ]),