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/TestView.vue

@@ -378,7 +378,7 @@ export default class Help extends Vue {
             this.userName = DEFAULT_USERNAME;
           },
           onYes: async () => {
-            (this.$router as Router).push({ name: "new-edit-account" });
+            this.$router.push({ name: "new-edit-account" });
           },
           noText: "try again and use " + DEFAULT_USERNAME,
         },