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)
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with [ReviewStack](https://reviewstack.dev/openai/codex/pull/2240).
* #2264
* #2263
* __->__ #2240

codex-rs/core/tests/compact.rs

@@ -1,7 +1,6 @@
 #![expect(clippy::unwrap_used)]
 
-use codex_core::Codex;
-use codex_core::CodexSpawnOk;
+use codex_core::ConversationManager;
 use codex_core::ModelProviderInfo;
 use codex_core::built_in_model_providers;
 use codex_core::protocol::EventMsg;
@@ -142,14 +141,12 @@ async fn summarize_context_three_requests_and_instructions() {
     let home = TempDir::new().unwrap();
     let mut config = load_default_config_for_test(&home);
     config.model_provider = model_provider;
-    let ctrl_c = std::sync::Arc::new(tokio::sync::Notify::new());
-    let CodexSpawnOk { codex, .. } = Codex::spawn(
-        config,
-        Some(CodexAuth::from_api_key("dummy")),
-        ctrl_c.clone(),
-    )
-    .await
-    .unwrap();
+    let conversation_manager = ConversationManager::default();
+    let codex = conversation_manager
+        .new_conversation_with_auth(config, Some(CodexAuth::from_api_key("dummy")))
+        .await
+        .unwrap()
+        .conversation;
 
     // 1) Normal user input – should hit server once.
     codex