refactor: improve router type safety and usage

- Add explicit Router type imports across views
- Replace $router type casting with proper typing
- Use $router.back() instead of $router.go(-1) for consistency
- Add proper route and router typings to components
- Clean up router navigation methods
- Fix router push/back method calls

This commit improves type safety and consistency in router usage across
the application's view components.

src/views/QuickActionBvcBeginView.vue

@@ -90,7 +90,7 @@ import * as libsUtil from "../libs/util";
 })
 export default class QuickActionBvcBeginView extends Vue {
   $notify!: (notification: NotificationIface, timeout?: number) => void;
-
+  $router!: Router;
   attended = true;
   gaveTime = true;
   hoursStr = "1";
@@ -201,7 +201,7 @@ export default class QuickActionBvcBeginView extends Vue {
           },
           3000,
         );
-        (this.$router as Router).push({ path: "/quick-action-bvc" });
+        this.$router.push({ path: "/quick-action-bvc" });
       }
 
       // eslint-disable-next-line @typescript-eslint/no-explicit-any