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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* #2264
* #2263
* __->__ #2240

codex-rs/core/src/error.rs

@@ -3,6 +3,7 @@ use serde_json;
 use std::io;
 use thiserror::Error;
 use tokio::task::JoinError;
+use uuid::Uuid;
 
 pub type Result<T> = std::result::Result<T, CodexErr>;
 
@@ -44,6 +45,12 @@ pub enum CodexErr {
     #[error("stream disconnected before completion: {0}")]
     Stream(String),
 
+    #[error("no conversation with id: {0}")]
+    ConversationNotFound(Uuid),
+
+    #[error("session configured event was not the first event in the stream")]
+    SessionConfiguredNotFirstEvent,
+
     /// Returned by run_command_stream when the spawned child process timed out (10s).
     #[error("timeout waiting for child process to exit")]
     Timeout,