docs: fix ScreenManager doctest after run method removal

- Update doctest example to use current API with with_instance and run_global
- Remove references to removed run() method
- Ensure all tests pass including doctests

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: unhappychoice

src/game/screen_manager.rs

@@ -15,18 +15,18 @@
 //! ## Usage Example
 //!
 //! ```rust,no_run
-//! use gittype::game::{ScreenManager, ScreenType, UpdateStrategy};
+//! use gittype::game::{ScreenManager, ScreenType};
 //! use gittype::game::screens::title_screen::TitleScreen;
 //!
-//! fn main() -> gittype::Result<()> {
-//!     let mut screen_manager = ScreenManager::new();
-//!     
+//! fn example() -> gittype::Result<()> {
 //!     let screen = TitleScreen::new();
 //!     
-//!     screen_manager.register_screen(ScreenType::Title, Box::new(screen));
-//!     screen_manager.run()?;
+//!     ScreenManager::with_instance(|manager| {
+//!         let mut manager = manager.borrow_mut();
+//!         manager.register_screen(ScreenType::Title, Box::new(screen));
+//!     });
 //!     
-//!     Ok(())
+//!     ScreenManager::run_global()
 //! }
 //! ```
 

src/game/screens/total_summary_screen.rs

@@ -111,8 +111,7 @@ impl Screen for TotalSummaryScreen {
         _total_result: Option<&crate::scoring::TotalResult>,
     ) -> Result<()> {
         if !self.displayed {
-            let total_result = Self::get_total_result_from_tracker()
-                .unwrap_or_default();
+            let total_result = Self::get_total_result_from_tracker().unwrap_or_default();
 
             let _ = TotalSummaryScreen::show(&total_result);
             self.displayed = true;