Tighten BTW fork cleanup

- fold interrupted snapshot behavior into the main fork API
- trim BTW tests that asserted internal channel/session details
- drop the app-server helper test for discard internals

Co-authored-by: Codex <noreply@openai.com>

codex-rs/core/tests/suite/compact_resume_fork.rs

@@ -12,6 +12,7 @@ use super::compact::FIRST_REPLY;
 use super::compact::SUMMARY_TEXT;
 use anyhow::Result;
 use codex_core::CodexThread;
+use codex_core::ForkSnapshot;
 use codex_core::ThreadManager;
 use codex_core::compact::SUMMARIZATION_PROMPT;
 use codex_core::config::Config;
@@ -858,8 +859,14 @@ async fn fork_thread(
     path: std::path::PathBuf,
     nth_user_message: usize,
 ) -> Arc<CodexThread> {
-    Box::pin(manager.fork_thread(nth_user_message, config.clone(), path, false, None))
-        .await
-        .expect("fork conversation")
-        .thread
+    Box::pin(manager.fork_thread(
+        ForkSnapshot::TruncateBeforeNthUserMessage(nth_user_message),
+        config.clone(),
+        path,
+        /*persist_extended_history*/ false,
+        /*parent_trace*/ None,
+    ))
+    .await
+    .expect("fork conversation")
+    .thread
 }