[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/app-server/src/request_processors/thread_processor.rs

@@ -4154,7 +4154,7 @@ fn summary_from_thread_metadata(metadata: &ThreadMetadata) -> ConversationSummar
         metadata.cwd.clone(),
         metadata.cli_version.clone(),
         metadata.source.clone(),
-        metadata.thread_source,
+        metadata.thread_source.clone(),
         metadata.agent_nickname.clone(),
         metadata.agent_role.clone(),
         metadata.git_sha.clone(),
@@ -4243,7 +4243,7 @@ fn build_thread_from_snapshot(
         agent_nickname: config_snapshot.session_source.get_nickname(),
         agent_role: config_snapshot.session_source.get_agent_role(),
         source: config_snapshot.session_source.clone().into(),
-        thread_source: config_snapshot.thread_source.map(Into::into),
+        thread_source: config_snapshot.thread_source.clone().map(Into::into),
         git_info: None,
         name: None,
         turns: Vec::new(),