IJPL-172200 IJPL-176167 prevent 'LaterInvocator.forceLeaveAllModals'-induced errors from cancelling IDE exit

(cherry picked from commit ee9547bb2963ffcdc7ebb832a7f28621cdcfe82f)
IJ-CR-156309

GitOrigin-RevId: 633c237c621400b1a9d48482f859b2931aee38b5

platform/configuration-store-impl/src/SaveAndSyncHandlerImpl.kt

@@ -285,6 +285,7 @@ private class SaveAndSyncHandlerImpl(private val coroutineScope: CoroutineScope)
         title = getProgressTitle(componentManager),
         cancellation = TaskCancellation.nonCancellable(),
       ) {
+        withContext(NonCancellable) {
           // ensure that is fully canceled
           currentJob?.join()
 
@@ -298,6 +299,7 @@ private class SaveAndSyncHandlerImpl(private val coroutineScope: CoroutineScope)
           }
         }
       }
+    }
 
     if (isAutoSaveCancelled) {
       requestSave()

platform/platform-impl/src/com/intellij/openapi/application/impl/ApplicationImpl.java

@@ -674,9 +674,14 @@ public final class ApplicationImpl extends ClientAwareComponentManager implement
       stopServicePreloading();
 
       if (BitUtil.isSet(flags, SAVE)) {
+        try {
           TraceKt.use(tracer.spanBuilder("saveSettingsOnExit"),
                       __ -> SaveAndSyncHandler.getInstance().saveSettingsUnderModalProgress(this));
         }
+        catch (Throwable e) {
+          logErrorDuringExit("Failed to save settings", e);
+        }
+      }
 
       if (isInstantShutdownPossible()) {
         for (Frame frame : Frame.getFrames()) {

platform/progress/shared/src/TaskCancellation.kt

@@ -23,6 +23,8 @@ sealed interface TaskCancellation {
   companion object {
     /**
      * @return a cancellation instance, which means that the cancel button should not be displayed in the UI
+     *
+     * It does not indicate that the task is inside [kotlinx.coroutines.NonCancellable] section.
      */
     @Contract(pure = true)
     @JvmStatic