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/HelpView.vue

@@ -588,6 +588,7 @@ import {
 @Component({ components: { QuickNav } })
 export default class Help extends Vue {
   $notify!: (notification: NotificationIface, timeout?: number) => void;
+  $router!: Router;
 
   package = Package;
   commitHash = import.meta.env.VITE_GIT_HASH;
@@ -614,7 +615,7 @@ export default class Help extends Vue {
         finishedOnboarding: false,
       });
     }
-    (this.$router as Router).push({ name: "home" });
+    this.$router.push({ name: "home" });
   }
 }
 </script>