[codex-tui] pass thread source for tui threads (#21401)

## Summary
- mark TUI-created thread starts and forks with explicit `thread_source
= user`
- add focused coverage for embedded and remote lifecycle request
builders

## Why
Thread analytics now consume an explicit thread-level source
classification instead of inferring it from `session_source`. The TUI
still omitted that field, so TUI-created interactive threads would
continue to land as `null` even after the new analytics plumbing
shipped.

## Validation
- `cargo test -p codex-tui app_server_session --lib`

codex-rs/tui/src/app_server_session.rs

@@ -87,6 +87,7 @@ use codex_app_server_protocol::ThreadSetNameParams;
 use codex_app_server_protocol::ThreadSetNameResponse;
 use codex_app_server_protocol::ThreadShellCommandParams;
 use codex_app_server_protocol::ThreadShellCommandResponse;
+use codex_app_server_protocol::ThreadSource;
 use codex_app_server_protocol::ThreadStartParams;
 use codex_app_server_protocol::ThreadStartResponse;
 use codex_app_server_protocol::ThreadStartSource;
@@ -1195,6 +1196,7 @@ fn thread_start_params_from_config(
         config: config_request_overrides_from_config(config),
         ephemeral: Some(config.ephemeral),
         session_start_source,
+        thread_source: Some(ThreadSource::User),
         persist_extended_history: false,
         ..ThreadStartParams::default()
     }
@@ -1260,6 +1262,7 @@ fn thread_fork_params_from_config(
         base_instructions: config.base_instructions.clone(),
         developer_instructions: config.developer_instructions.clone(),
         ephemeral: config.ephemeral,
+        thread_source: Some(ThreadSource::User),
         persist_extended_history: false,
         ..ThreadForkParams::default()
     }
@@ -1561,6 +1564,7 @@ mod tests {
                 .map(permissions_selection_from_active_profile)
         );
         assert_eq!(params.model_provider, Some(config.model_provider_id));
+        assert_eq!(params.thread_source, Some(ThreadSource::User));
     }
 
     #[tokio::test]
@@ -1677,6 +1681,8 @@ mod tests {
         assert_eq!(start.permissions, None);
         assert_eq!(resume.permissions, None);
         assert_eq!(fork.permissions, None);
+        assert_eq!(start.thread_source, Some(ThreadSource::User));
+        assert_eq!(fork.thread_source, Some(ThreadSource::User));
     }
 
     #[test]
@@ -1782,6 +1788,8 @@ mod tests {
         assert_eq!(start.permissions, None);
         assert_eq!(resume.permissions, None);
         assert_eq!(fork.permissions, None);
+        assert_eq!(start.thread_source, Some(ThreadSource::User));
+        assert_eq!(fork.thread_source, Some(ThreadSource::User));
     }
 
     #[tokio::test]