refactor: extract main runtime helper groups

- Extract remaining runtime helper clusters from main.ts into dedicated modules for readability:\n  - src/main/jlpt-runtime.ts\n  - src/main/media-runtime.ts\n  - src/main/overlay-visibility-runtime.ts\n- Wire main.ts to use the new runtime services and remove duplicated in-file helpers.\n- Preserve existing behavior via full typecheck + test:fast verification.\n- Finalize and archive TASK-56 backlog entry; update TASK-54 with completion metadata and summary.

src/main/overlay-visibility-runtime.ts

@@ -0,0 +1,92 @@
+import type { BrowserWindow } from "electron";
+
+import type { BaseWindowTracker } from "../window-trackers";
+import type { WindowGeometry } from "../types";
+import {
+  syncInvisibleOverlayMousePassthroughService,
+  updateInvisibleOverlayVisibilityService,
+  updateVisibleOverlayVisibilityService,
+} from "../core/services";
+
+export interface OverlayVisibilityRuntimeDeps {
+  getMainWindow: () => BrowserWindow | null;
+  getInvisibleWindow: () => BrowserWindow | null;
+  getVisibleOverlayVisible: () => boolean;
+  getInvisibleOverlayVisible: () => boolean;
+  getWindowTracker: () => BaseWindowTracker | null;
+  getTrackerNotReadyWarningShown: () => boolean;
+  setTrackerNotReadyWarningShown: (shown: boolean) => void;
+  updateVisibleOverlayBounds: (geometry: WindowGeometry) => void;
+  updateInvisibleOverlayBounds: (geometry: WindowGeometry) => void;
+  ensureOverlayWindowLevel: (window: BrowserWindow) => void;
+  enforceOverlayLayerOrder: () => void;
+  syncOverlayShortcuts: () => void;
+}
+
+export interface OverlayVisibilityRuntimeService {
+  updateVisibleOverlayVisibility: () => void;
+  updateInvisibleOverlayVisibility: () => void;
+  syncInvisibleOverlayMousePassthrough: () => void;
+}
+
+export function createOverlayVisibilityRuntimeService(
+  deps: OverlayVisibilityRuntimeDeps,
+): OverlayVisibilityRuntimeService {
+  const hasInvisibleWindow = (): boolean => {
+    const invisibleWindow = deps.getInvisibleWindow();
+    return Boolean(invisibleWindow && !invisibleWindow.isDestroyed());
+  };
+
+  const setIgnoreMouseEvents = (
+    ignore: boolean,
+    options?: Parameters<BrowserWindow["setIgnoreMouseEvents"]>[1],
+  ): void => {
+    const invisibleWindow = deps.getInvisibleWindow();
+    if (!invisibleWindow || invisibleWindow.isDestroyed()) return;
+    invisibleWindow.setIgnoreMouseEvents(ignore, options);
+  };
+
+  return {
+    updateVisibleOverlayVisibility(): void {
+      updateVisibleOverlayVisibilityService({
+        visibleOverlayVisible: deps.getVisibleOverlayVisible(),
+        mainWindow: deps.getMainWindow(),
+        windowTracker: deps.getWindowTracker(),
+        trackerNotReadyWarningShown: deps.getTrackerNotReadyWarningShown(),
+        setTrackerNotReadyWarningShown: (shown: boolean) => {
+          deps.setTrackerNotReadyWarningShown(shown);
+        },
+        updateVisibleOverlayBounds: (geometry: WindowGeometry) =>
+          deps.updateVisibleOverlayBounds(geometry),
+        ensureOverlayWindowLevel: (window: BrowserWindow) =>
+          deps.ensureOverlayWindowLevel(window),
+        enforceOverlayLayerOrder: () => deps.enforceOverlayLayerOrder(),
+        syncOverlayShortcuts: () => deps.syncOverlayShortcuts(),
+      });
+    },
+
+    updateInvisibleOverlayVisibility(): void {
+      updateInvisibleOverlayVisibilityService({
+        invisibleWindow: deps.getInvisibleWindow(),
+        visibleOverlayVisible: deps.getVisibleOverlayVisible(),
+        invisibleOverlayVisible: deps.getInvisibleOverlayVisible(),
+        windowTracker: deps.getWindowTracker(),
+        updateInvisibleOverlayBounds: (geometry: WindowGeometry) =>
+          deps.updateInvisibleOverlayBounds(geometry),
+        ensureOverlayWindowLevel: (window: BrowserWindow) =>
+          deps.ensureOverlayWindowLevel(window),
+        enforceOverlayLayerOrder: () => deps.enforceOverlayLayerOrder(),
+        syncOverlayShortcuts: () => deps.syncOverlayShortcuts(),
+      });
+    },
+
+    syncInvisibleOverlayMousePassthrough(): void {
+      syncInvisibleOverlayMousePassthroughService({
+        hasInvisibleWindow,
+        setIgnoreMouseEvents,
+        visibleOverlayVisible: deps.getVisibleOverlayVisible(),
+        invisibleOverlayVisible: deps.getInvisibleOverlayVisible(),
+      });
+    },
+  };
+}