[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/core/src/session/session.rs

@@ -193,7 +193,7 @@ impl SessionConfiguration {
             session_source: self.session_source.clone(),
             forked_from_thread_id: self.forked_from_thread_id,
             parent_thread_id: self.parent_thread_id,
-            thread_source: self.thread_source,
+            thread_source: self.thread_source.clone(),
         }
     }
 
@@ -549,7 +549,7 @@ impl Session {
                                 forked_from_id,
                                 parent_thread_id,
                                 source: session_source,
-                                thread_source: session_configuration.thread_source,
+                                thread_source: session_configuration.thread_source.clone(),
                                 base_instructions: BaseInstructions {
                                     text: session_configuration.base_instructions.clone(),
                                 },
@@ -1089,7 +1089,7 @@ impl Session {
                     thread_id,
                     forked_from_id,
                     parent_thread_id,
-                    thread_source: session_configuration.thread_source,
+                    thread_source: session_configuration.thread_source.clone(),
                     thread_name: session_configuration.thread_name.clone(),
                     model: session_configuration.collaboration_mode.model().to_string(),
                     model_provider_id: config.model_provider_id.clone(),