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/thread-store/src/local/update_thread_metadata.rs

@@ -204,6 +204,7 @@ async fn apply_metadata_update(
                     .map_err(|err| ThreadStoreError::Internal {
                         message: format!("failed to read thread metadata for {thread_id}: {err}"),
                     })?;
+            let advance_recency_at = patch.advance_recency_at;
             if existing.is_none() && rollout_path.is_none() {
                 let resolved = resolve_rollout_path(store, thread_id, include_archived).await?;
                 rollout_path_archived = resolved.archived;
@@ -260,6 +261,11 @@ async fn apply_metadata_update(
             if let Some(updated_at) = patch.updated_at {
                 metadata.updated_at = updated_at;
             }
+            if existing.is_none()
+                && let Some(recency_at) = advance_recency_at
+            {
+                metadata.recency_at = recency_at;
+            }
             if let Some(source) = patch.source {
                 metadata.source = enum_to_string(&source);
             }
@@ -310,6 +316,18 @@ async fn apply_metadata_update(
                 .map_err(|err| ThreadStoreError::Internal {
                     message: format!("failed to update thread metadata for {thread_id}: {err}"),
                 })?;
+            if existing.is_some()
+                && let Some(recency_at) = advance_recency_at
+            {
+                state_db
+                    .touch_thread_recency_at(thread_id, recency_at)
+                    .await
+                    .map_err(|err| ThreadStoreError::Internal {
+                        message: format!(
+                            "failed to advance thread recency_at for {thread_id}: {err}"
+                        ),
+                    })?;
+            }
             if let Some(memory_mode) = patch.memory_mode {
                 state_db
                     .set_thread_memory_mode(thread_id, memory_mode_as_str(memory_mode))