Revert App::run() behavior/Remove winit specific code from bevy_app (#10389)

# Objective
The way `bevy_app` works was changed unnecessarily in #9826 whose
changes should have been specific to `bevy_winit`.
I'm somewhat disappointed that happened and we can see in
https://github.com/bevyengine/bevy/pull/10195 that it made things more
complicated.

Even worse, in #10385 it's clear that this breaks the clean abstraction
over another engine someone built with Bevy!

Fixes #10385.

## Solution

- Move the changes made to `bevy_app` in #9826 to `bevy_winit`
- Revert the changes to `ScheduleRunnerPlugin` and the `run_once` runner
in #10195 as they're no longer necessary.

While this code is breaking relative to `0.12.0`, it reverts the
behavior of `bevy_app` back to how it was in `0.11`.
Due to the nature of the breakage relative to `0.11` I hope this will be
considered for `0.12.1`.

crates/bevy_app/src/app.rs

@@ -309,14 +309,6 @@ impl App {
             panic!("App::run() was called from within Plugin::build(), which is not allowed.");
         }
 
-        if app.plugins_state() == PluginsState::Ready {
-            // If we're already ready, we finish up now and advance one frame.
-            // This prevents black frames during the launch transition on iOS.
-            app.finish();
-            app.cleanup();
-            app.update();
-        }
-
         let runner = std::mem::replace(&mut app.runner, Box::new(run_once));
         (runner)(app);
     }
@@ -986,20 +978,14 @@ impl App {
 }
 
 fn run_once(mut app: App) {
-    let plugins_state = app.plugins_state();
+    while app.plugins_state() == PluginsState::Adding {
-    if plugins_state != PluginsState::Cleaned {
+        #[cfg(not(target_arch = "wasm32"))]
-        while app.plugins_state() == PluginsState::Adding {
+        bevy_tasks::tick_global_task_pools_on_main_thread();
-            #[cfg(not(target_arch = "wasm32"))]
-            bevy_tasks::tick_global_task_pools_on_main_thread();
-        }
-        app.finish();
-        app.cleanup();
     }
+    app.finish();
+    app.cleanup();
 
-    // if plugins where cleaned before the runner start, an update already ran
+    app.update();
-    if plugins_state != PluginsState::Cleaned {
-        app.update();
-    }
 }
 
 /// An event that indicates the [`App`] should exit. This will fully exit the app process at the

crates/bevy_app/src/schedule_runner.rs

@@ -84,12 +84,7 @@ impl Plugin for ScheduleRunnerPlugin {
 
             let mut app_exit_event_reader = ManualEventReader::<AppExit>::default();
             match run_mode {
-                RunMode::Once => {
+                RunMode::Once => app.update(),
-                    // if plugins where cleaned before the runner start, an update already ran
-                    if plugins_state != PluginsState::Cleaned {
-                        app.update();
-                    }
-                }
                 RunMode::Loop { wait } => {
                     let mut tick = move |app: &mut App,
                                          wait: Option<Duration>|

crates/bevy_winit/src/lib.rs

@@ -349,6 +349,14 @@ impl Default for WinitAppRunnerState {
 /// Overriding the app's [runner](bevy_app::App::runner) while using `WinitPlugin` will bypass the
 /// `EventLoop`.
 pub fn winit_runner(mut app: App) {
+    if app.plugins_state() == PluginsState::Ready {
+        // If we're already ready, we finish up now and advance one frame.
+        // This prevents black frames during the launch transition on iOS.
+        app.finish();
+        app.cleanup();
+        app.update();
+    }
+
     let mut event_loop = app
         .world
         .remove_non_send_resource::<EventLoop<()>>()