[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/in_memory.rs

@@ -177,7 +177,7 @@ impl ThreadStore for InMemoryThreadStore {
             agent_role: params.source.get_agent_role(),
             agent_path: params.source.get_agent_path().map(Into::into),
             source: params.source.clone(),
-            thread_source: params.thread_source,
+            thread_source: params.thread_source.clone(),
             model_provider: Some(params.metadata.model_provider.clone()),
             base_instructions: Some(params.base_instructions.clone()),
             dynamic_tools: (!params.dynamic_tools.is_empty()).then(|| params.dynamic_tools.clone()),
@@ -392,8 +392,8 @@ fn stored_thread_from_state(
             .and_then(|metadata| metadata.source.clone())
             .unwrap_or_else(|| created.source.clone()),
         thread_source: metadata
-            .and_then(|metadata| metadata.thread_source)
-            .unwrap_or(created.thread_source),
+            .and_then(|metadata| metadata.thread_source.clone())
+            .unwrap_or_else(|| created.thread_source.clone()),
         agent_nickname: metadata.and_then(|metadata| metadata.agent_nickname.clone().flatten()),
         agent_role: metadata.and_then(|metadata| metadata.agent_role.clone().flatten()),
         agent_path: metadata.and_then(|metadata| metadata.agent_path.clone().flatten()),