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/tests.rs

@@ -612,6 +612,7 @@ async fn test_list_conversations_latest_first() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some("2025-01-03T12-00-00".into()),
+                recency_at: updated_times.first().cloned().flatten(),
                 updated_at: updated_times.first().cloned().flatten(),
             },
             ThreadItem {
@@ -630,6 +631,7 @@ async fn test_list_conversations_latest_first() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some("2025-01-02T12-00-00".into()),
+                recency_at: updated_times.get(1).cloned().flatten(),
                 updated_at: updated_times.get(1).cloned().flatten(),
             },
             ThreadItem {
@@ -648,6 +650,7 @@ async fn test_list_conversations_latest_first() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some("2025-01-01T12-00-00".into()),
+                recency_at: updated_times.get(2).cloned().flatten(),
                 updated_at: updated_times.get(2).cloned().flatten(),
             },
         ],
@@ -759,6 +762,7 @@ async fn test_pagination_cursor() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some("2025-03-05T09-00-00".into()),
+                recency_at: updated_page1.first().cloned().flatten(),
                 updated_at: updated_page1.first().cloned().flatten(),
             },
             ThreadItem {
@@ -777,6 +781,7 @@ async fn test_pagination_cursor() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some("2025-03-04T09-00-00".into()),
+                recency_at: updated_page1.get(1).cloned().flatten(),
                 updated_at: updated_page1.get(1).cloned().flatten(),
             },
         ],
@@ -831,6 +836,7 @@ async fn test_pagination_cursor() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some("2025-03-03T09-00-00".into()),
+                recency_at: updated_page2.first().cloned().flatten(),
                 updated_at: updated_page2.first().cloned().flatten(),
             },
             ThreadItem {
@@ -849,6 +855,7 @@ async fn test_pagination_cursor() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some("2025-03-02T09-00-00".into()),
+                recency_at: updated_page2.get(1).cloned().flatten(),
                 updated_at: updated_page2.get(1).cloned().flatten(),
             },
         ],
@@ -895,6 +902,7 @@ async fn test_pagination_cursor() {
             model_provider: Some(TEST_PROVIDER.to_string()),
             cli_version: Some("test_version".to_string()),
             created_at: Some("2025-03-01T09-00-00".into()),
+            recency_at: updated_page3.first().cloned().flatten(),
             updated_at: updated_page3.first().cloned().flatten(),
         }],
         next_cursor: None,
@@ -1066,6 +1074,7 @@ async fn test_get_thread_contents() {
             model_provider: Some(TEST_PROVIDER.to_string()),
             cli_version: Some("test_version".to_string()),
             created_at: Some(ts.into()),
+            recency_at: page.items[0].updated_at.clone(),
             updated_at: page.items[0].updated_at.clone(),
         }],
         next_cursor: None,
@@ -1421,6 +1430,7 @@ async fn test_timestamp_only_cursor_skips_same_second_filesystem_ties() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some(ts.to_string()),
+                recency_at: updated_page1.first().cloned().flatten(),
                 updated_at: updated_page1.first().cloned().flatten(),
             },
             ThreadItem {
@@ -1439,6 +1449,7 @@ async fn test_timestamp_only_cursor_skips_same_second_filesystem_ties() {
                 model_provider: Some(TEST_PROVIDER.to_string()),
                 cli_version: Some("test_version".to_string()),
                 created_at: Some(ts.to_string()),
+                recency_at: updated_page1.get(1).cloned().flatten(),
                 updated_at: updated_page1.get(1).cloned().flatten(),
             },
         ],