Revert thread recencyAt for sidebar ordering (#28655)

## Why

Revert #27910 to remove the newly introduced thread `recencyAt`
persistence and API behavior from `main`.

## What changed

This reverts commit `fac3158c2a783095768076489815f361fa9b0db4`,
including the state migration, thread-store propagation, app-server API
surface, generated schemas, and related tests.

## Validation

Not run before opening; relying on CI for the initial fast signal.

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -2501,7 +2501,6 @@ mod tests {
                     model_provider: "openai".to_string(),
                     created_at: 1,
                     updated_at: 2,
-                    recency_at: Some(3),
                     status: v2::ThreadStatus::Idle,
                     path: None,
                     cwd: cwd.clone(),
@@ -2545,7 +2544,6 @@ mod tests {
                         "modelProvider": "openai",
                         "createdAt": 1,
                         "updatedAt": 2,
-                        "recencyAt": 3,
                         "status": {
                             "type": "idle"
                         },

codex-rs/app-server-protocol/src/protocol/v2/tests.rs

@@ -174,7 +174,6 @@ fn thread_resume_response_round_trips_initial_turns_page() {
             model_provider: "openai".to_string(),
             created_at: 1,
             updated_at: 1,
-            recency_at: Some(1),
             status: ThreadStatus::Idle,
             path: None,
             cwd: absolute_path("tmp"),
@@ -3601,7 +3600,6 @@ fn thread_lifecycle_responses_default_missing_optional_fields() {
 
     assert_eq!(start.instruction_sources, Vec::<AbsolutePathBuf>::new());
     assert_eq!(start.thread.parent_thread_id, None);
-    assert_eq!(start.thread.recency_at, None);
     assert_eq!(resume.instruction_sources, Vec::<AbsolutePathBuf>::new());
     assert_eq!(fork.instruction_sources, Vec::<AbsolutePathBuf>::new());
     assert_eq!(start.active_permission_profile, None);
@@ -3610,14 +3608,6 @@ fn thread_lifecycle_responses_default_missing_optional_fields() {
     assert_eq!(fork.active_permission_profile, None);
 }
 
-#[test]
-fn thread_recency_sort_key_serializes_as_snake_case() {
-    assert_eq!(
-        serde_json::to_value(ThreadSortKey::RecencyAt).expect("sort key should serialize"),
-        json!("recency_at")
-    );
-}
-
 #[test]
 fn turn_start_params_preserve_explicit_null_service_tier() {
     let params: TurnStartParams = serde_json::from_value(json!({

codex-rs/app-server-protocol/src/protocol/v2/thread.rs

@@ -1086,7 +1086,6 @@ pub enum ThreadSourceKind {
 pub enum ThreadSortKey {
     CreatedAt,
     UpdatedAt,
-    RecencyAt,
 }
 
 #[derive(Serialize, Deserialize, Debug, Clone, Copy, PartialEq, JsonSchema, TS)]

codex-rs/app-server-protocol/src/protocol/v2/thread_data.rs

@@ -152,9 +152,6 @@ pub struct Thread {
     /// Unix timestamp (in seconds) when the thread was last updated.
     #[ts(type = "number")]
     pub updated_at: i64,
-    /// Unix timestamp (in seconds) used for thread recency ordering.
-    #[ts(type = "number | null")]
-    pub recency_at: Option<i64>,
     /// Current runtime status for the thread.
     pub status: ThreadStatus,
     /// [UNSTABLE] Path to the thread on disk.