…fy WelcomeScene

- Move /btw side-question turn persistence from frontend to Rust backend:
  add persist_btw_turn to SessionManager and Coordinator, expose via
  BtwAskStreamRequest and remove inline saveSessionTurn logic from BtwThreadService
- Add per-workspace mutex (SESSION_INDEX_LOCKS) in PersistenceManager to
  prevent session-index races; detect and rebuild stale index entries;
  fix metadata-before-write ordering in save_dialog_turn
- Add cleanup_invalid_workspaces Tauri command and save workspace data after
  cleanup in workspace service; call it on app startup in workspaceManager
- Refactor WelcomeScene into a single unified view, removing has-workspace /
  first-time split, panda mascot, session-type buttons, and git branch tag;
  update locales (en-US / zh-CN) accordingly
- Minor UI polish: NavPanel, SplashScreen, PersonaView, ChatInput styles

GCWing changed the title feat: move /btw persistence to backend, add workspace cleanup, simpli… feat: move /btw persistence to backend, add workspace cleanup, simplify WelcomeScene