chore: introduce ConversationManager as a clearinghouse for all conversations (#2240)

This PR does two things because after I got deep into the first one I
started pulling on the thread to the second:

- Makes `ConversationManager` the place where all in-memory
conversations are created and stored. Previously, `MessageProcessor` in
the `codex-mcp-server` crate was doing this via its `session_map`, but
this is something that should be done in `codex-core`.
- It unwinds the `ctrl_c: tokio::sync::Notify` that was threaded
throughout our code. I think this made sense at one time, but now that
we handle Ctrl-C within the TUI and have a proper `Op::Interrupt` event,
I don't think this was quite right, so I removed it. For `codex exec`
and `codex proto`, we now use `tokio::signal::ctrl_c()` directly, but we
no longer make `Notify` a field of `Codex` or `CodexConversation`.

Changes of note:

- Adds the files `conversation_manager.rs` and `codex_conversation.rs`
to `codex-core`.
- `Codex` and `CodexSpawnOk` are no longer exported from `codex-core`:
other crates must use `CodexConversation` instead (which is created via
`ConversationManager`).
- `core/src/codex_wrapper.rs` has been deleted in favor of
`ConversationManager`.
- `ConversationManager::new_conversation()` returns `NewConversation`,
which is in line with the `new_conversation` tool we want to add to the
MCP server. Note `NewConversation` includes `SessionConfiguredEvent`, so
we eliminate checks in cases like `codex-rs/core/tests/client.rs` to
verify `SessionConfiguredEvent` is the first event because that is now
internal to `ConversationManager`.
- Quite a bit of code was deleted from
`codex-rs/mcp-server/src/message_processor.rs` since it no longer has to
manage multiple conversations itself: it goes through
`ConversationManager` instead.
- `core/tests/live_agent.rs` has been deleted because I had to update a
bunch of tests and all the tests in here were ignored, and I don't think
anyone ever ran them, so this was just technical debt, at this point.
- Removed `notify_on_sigint()` from `util.rs` (and in a follow-up, I
hope to refactor the blandly-named `util.rs` into more descriptive
files).
- In general, I started replacing local variables named `codex` as
`conversation`, where appropriate, though admittedly I didn't do it
through all the integration tests because that would have added a lot of
noise to this PR.




---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/2240).
* #2264
* #2263
* __->__ #2240

codex-rs/tui/src/app.rs

@@ -9,6 +9,7 @@ use crate::onboarding::onboarding_screen::OnboardingScreenArgs;
 use crate::should_show_login_screen;
 use crate::slash_command::SlashCommand;
 use crate::tui;
+use codex_core::ConversationManager;
 use codex_core::config::Config;
 use codex_core::protocol::Event;
 use codex_core::protocol::Op;
@@ -48,6 +49,7 @@ enum AppState<'a> {
 }
 
 pub(crate) struct App<'a> {
+    server: Arc<ConversationManager>,
     app_event_tx: AppEventSender,
     app_event_rx: Receiver<AppEvent>,
     app_state: AppState<'a>,
@@ -85,6 +87,8 @@ impl App<'_> {
         initial_images: Vec<std::path::PathBuf>,
         show_trust_screen: bool,
     ) -> Self {
+        let conversation_manager = Arc::new(ConversationManager::default());
+
         let (app_event_tx, app_event_rx) = channel();
         let app_event_tx = AppEventSender::new(app_event_tx);
         let pending_redraw = Arc::new(AtomicBool::new(false));
@@ -153,6 +157,7 @@ impl App<'_> {
         } else {
             let chat_widget = ChatWidget::new(
                 config.clone(),
+                conversation_manager.clone(),
                 app_event_tx.clone(),
                 initial_prompt,
                 initial_images,
@@ -165,6 +170,7 @@ impl App<'_> {
 
         let file_search = FileSearchManager::new(config.cwd.clone(), app_event_tx.clone());
         Self {
+            server: conversation_manager,
             app_event_tx,
             pending_history_lines: Vec::new(),
             app_event_rx,
@@ -328,6 +334,7 @@ impl App<'_> {
                         // User accepted – switch to chat view.
                         let new_widget = Box::new(ChatWidget::new(
                             self.config.clone(),
+                            self.server.clone(),
                             self.app_event_tx.clone(),
                             None,
                             Vec::new(),
@@ -449,6 +456,7 @@ impl App<'_> {
                     self.app_state = AppState::Chat {
                         widget: Box::new(ChatWidget::new(
                             config,
+                            self.server.clone(),
                             app_event_tx.clone(),
                             initial_prompt,
                             initial_images,