[codex-analytics] add extensible feature thread sources (#27063)

## Why
- `ThreadSource` currently defines a closed set of core-owned values
- Product features also create threads for background or scheduled work
- Adding every product-specific value to the core enum would require
repeated `codex-rs` protocol changes
- Feature-backed values let product callers provide precise attribution
while preserving the existing core classifications

## What Changed
- Adds `ThreadSource::Feature(String)` for app-owned thread source
values
- Represents all app-server v2 thread sources as scalar strings, so a
feature source is supplied as `"automation"`
- Persists and emits the feature's plain string label, so `"automation"`
produces `thread_source="automation"` in analytics
- Keeps `user`, `subagent`, and `memory_consolidation` as explicit
core-owned values and regenerates the app-server schemas and TypeScript
bindings

## Verification
- `just write-app-server-schema`
- `cargo check --workspace`
- `just test -p codex-protocol
feature_thread_source_serializes_as_its_app_owned_label`
- `just test -p codex-app-server-protocol
thread_sources_round_trip_as_scalar_labels`
- `cargo test -p codex-analytics
thread_initialized_event_serializes_expected_shape`
- `just fmt`

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

@@ -66,7 +66,7 @@ impl ThreadMetadataSync {
             created_at: Some(created_at),
             updated_at: Some(created_at),
             source: Some(params.source.clone()),
-            thread_source: Some(params.thread_source),
+            thread_source: Some(params.thread_source.clone()),
             agent_nickname: Some(params.source.get_nickname()),
             agent_role: Some(params.source.get_agent_role()),
             agent_path: Some(params.source.get_agent_path().map(Into::into)),
@@ -201,7 +201,7 @@ impl ThreadMetadataSync {
                 RolloutItem::SessionMeta(meta_line) if meta_line.meta.id == self.thread_id => {
                     update.created_at = parse_session_timestamp(meta_line.meta.timestamp.as_str());
                     update.source = Some(meta_line.meta.source.clone());
-                    update.thread_source = Some(meta_line.meta.thread_source);
+                    update.thread_source = Some(meta_line.meta.thread_source.clone());
                     update.agent_nickname = Some(meta_line.meta.agent_nickname.clone());
                     update.agent_role = Some(meta_line.meta.agent_role.clone());
                     update.agent_path = Some(meta_line.meta.agent_path.clone());