Rename lyricsx_style_app → applyrx_ui, fix in-process lyrics loading

- Rename lyricsx_style_app.py → applyrx_ui.py (no more LyricsX references)
- Rename run_lyricsx_ui.sh → run_applyrx.sh
- Replace subprocess readHelperState with direct in-process applyrx_state call
  (fixes ModuleNotFoundError: No module named 'rich' in bundled app)
- Fix self.error initial value from "LyricsX" to ""
- Fix LOG_PATH name to /tmp/applyrx.log
- Fix PROJECT_DIR detection for bundled .app via _find_project_dir()
- Update all docs and scripts

Co-Authored-By: Claude Sonnet 4.6 <[email protected]>