Add thread recencyAt for sidebar ordering (#27910)

## Summary

Add a server-owned `recencyAt` timestamp and `recency_at` thread-list
sort key for product recency ordering while preserving the existing
meaning of `updatedAt` as the latest persisted thread mutation.

This is the server-side alternative to #27697. Rather than narrowing
`updatedAt`, clients can sort the sidebar by `recency_at` and continue
treating `updatedAt` as mutation time.

Paired Codex Apps PR:
[openai/openai#1024599](https://github.com/openai/openai/pull/1024599)

## Contract

- `recencyAt` initializes when a thread is created.
- A turn start advances `recencyAt` monotonically.
- Commentary, agent output, tool results, token/accounting updates, turn
completion, archive, unarchive, resume, and generic metadata writes do
not advance it.
- `updatedAt` retains its existing behavior and continues to advance for
persisted thread mutations.
- Current servers populate `recencyAt`; the response field is optional
in generated TypeScript so clients connected to older servers can fall
back to `updatedAt`.
- Filesystem-only fallback uses existing updated/mtime ordering when
SQLite is unavailable.

## Persistence and compatibility

Migration 0038 adds second- and millisecond-precision recency columns,
backfills them from the existing updated timestamp, creates list
indexes, and includes an insert trigger so older binaries writing to a
migrated database seed recency without causing later mutations to
advance it.

Generic metadata upserts preserve existing recency values. Turn-start
updates use a dedicated monotonic touch, and process-local allocation
keeps millisecond cursor values unique. State DB list, search, read,
filtered-list repair, rollout fallback propagation, and app-server
conversions all carry the new field.

## API

`Thread` responses include:

```ts
recencyAt?: number
```

`thread/list` and `thread/search` accept:

```json
{ "sortKey": "recency_at" }
```

Generated TypeScript and JSON schemas are included.

## Validation

- `just test -p codex-state` — 146 passed
- `just test -p codex-rollout` — 69 passed
- `just test -p codex-thread-store` — 81 passed
- `just test -p codex-app-server-protocol` — 231 passed
- Focused app-server list ordering, response mapping, archive/unarchive,
and resume lifecycle tests passed
- Scoped `just fix` for state, rollout, thread-store,
app-server-protocol, and app-server
- `just fmt`
- `git diff --check`
- Independent correctness, simplicity, elegance, security, and
test-quality reviews; actionable ordering, lifecycle, query-projection,
and timestamp-uniqueness findings were addressed

codex-rs/rollout/src/state_db.rs

@@ -290,7 +290,10 @@ fn cursor_to_anchor(cursor: Option<&Cursor>) -> Option<codex_state::Anchor> {
     let millis = cursor.timestamp().unix_timestamp_nanos() / 1_000_000;
     let millis = i64::try_from(millis).ok()?;
     let ts = chrono::DateTime::<Utc>::from_timestamp_millis(millis)?;
-    Some(codex_state::Anchor { ts })
+    Some(codex_state::Anchor {
+        ts,
+        id: cursor.thread_id(),
+    })
 }
 
 pub fn normalize_cwd_for_state_db(cwd: &Path) -> PathBuf {
@@ -336,6 +339,7 @@ pub async fn list_thread_ids_db(
             match sort_key {
                 ThreadSortKey::CreatedAt => codex_state::SortKey::CreatedAt,
                 ThreadSortKey::UpdatedAt => codex_state::SortKey::UpdatedAt,
+                ThreadSortKey::RecencyAt => codex_state::SortKey::RecencyAt,
             },
             allowed_sources.as_slice(),
             model_providers.as_deref(),
@@ -401,6 +405,7 @@ pub async fn list_threads_db(
         sort_key: match sort_key {
             ThreadSortKey::CreatedAt => codex_state::SortKey::CreatedAt,
             ThreadSortKey::UpdatedAt => codex_state::SortKey::UpdatedAt,
+            ThreadSortKey::RecencyAt => codex_state::SortKey::RecencyAt,
         },
         sort_direction: match sort_direction {
             SortDirection::Asc => codex_state::SortDirection::Asc,