[codex] Route live thread writes through ThreadStore (#18882)

Begin migrating the thread write codepaths to ThreadStore.

This starts using ThreadStore inside of core session code, not only in
the app server code.

Rework the interfaces around thread recording/persistence. We're left
with the following:

* `ThreadManager`: owns the process-level registry of loaded threads and
handles cross-thread orchestration: start, resume, fork, lookup, remove,
and route ops to running CodexThreads.
* `CodexThread`: represents one loaded/running thread from the outside.
It is the handle app-server and callers use to submit ops, inspect
session metadata, and shut the thread down.
* `LiveThread`: session-owned persistence lifecycle handle for one
active thread. Core session code uses it to append rollout items,
materialize lazy persistence, flush, shutdown, discard init-failed
writers, and load that thread’s persisted history.
* `ThreadStore`: storage backend abstraction. It answers “how are
threads persisted, read, listed, updated, archived?” Local and remote
implementations live behind this trait.
* `LocalThreadStore`: local ThreadStore implementation. It owns the
file/sqlite-specific details and keeps RolloutRecorder as a local
implementation detail.

This is a few too many Thread abstractions for my liking, but they do
all represent different concepts / needs / layers.

Migration note: in places where the core code explicitly requires a
path, rather than a thread ID, throw an error if we're running with a
remote store.

Cover the new local live-writer lifecycle with focused tests and
preserve app-server thread-start behavior, including ephemeral pathless
sessions.

codex-rs/thread-store/src/lib.rs

@@ -5,16 +5,17 @@
 //! any other backing store.
 
 mod error;
+mod live_thread;
 mod local;
-mod recorder;
 mod remote;
 mod store;
 mod types;
 
 pub use error::ThreadStoreError;
 pub use error::ThreadStoreResult;
+pub use live_thread::LiveThread;
+pub use live_thread::LiveThreadInitGuard;
 pub use local::LocalThreadStore;
-pub use recorder::ThreadRecorder;
 pub use remote::RemoteThreadStore;
 pub use store::ThreadStore;
 pub use types::AppendThreadItemsParams;
@@ -25,7 +26,7 @@ pub use types::ListThreadsParams;
 pub use types::LoadThreadHistoryParams;
 pub use types::OptionalStringPatch;
 pub use types::ReadThreadParams;
-pub use types::ResumeThreadRecorderParams;
+pub use types::ResumeThreadParams;
 pub use types::SortDirection;
 pub use types::StoredThread;
 pub use types::StoredThreadHistory;