Refine realtime startup context formatting (#13560)

## Summary
- group recent work by git repo when available, otherwise by directory
- render recent work as bounded user asks with per-thread cwd context
- exclude hidden files and directories from workspace trees

codex-rs/core/src/realtime_conversation.rs

@@ -5,6 +5,7 @@ use crate::codex::Session;
 use crate::default_client::default_headers;
 use crate::error::CodexErr;
 use crate::error::Result as CodexResult;
+use crate::realtime_context::build_realtime_startup_context;
 use async_channel::Receiver;
 use async_channel::Sender;
 use async_channel::TrySendError;
@@ -43,6 +44,7 @@ const AUDIO_IN_QUEUE_CAPACITY: usize = 256;
 const USER_TEXT_IN_QUEUE_CAPACITY: usize = 64;
 const HANDOFF_OUT_QUEUE_CAPACITY: usize = 64;
 const OUTPUT_EVENTS_QUEUE_CAPACITY: usize = 256;
+const REALTIME_STARTUP_CONTEXT_TOKEN_BUDGET: usize = 5_000;
 
 pub(crate) struct RealtimeConversationManager {
     state: Mutex<Option<ConversationState>>,
@@ -282,6 +284,13 @@ pub(crate) async fn handle_start(
         .experimental_realtime_ws_backend_prompt
         .clone()
         .unwrap_or(params.prompt);
+    let prompt =
+        match build_realtime_startup_context(sess.as_ref(), REALTIME_STARTUP_CONTEXT_TOKEN_BUDGET)
+            .await
+        {
+            Some(context) => format!("{prompt}\n\n{context}"),
+            None => prompt,
+        };
     let model = config.experimental_realtime_ws_model.clone();
 
     let requested_session_id = params