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/UserProfileView.vue

@@ -9,7 +9,7 @@
       <h1 id="ViewHeading" class="text-lg text-center font-light relative px-7">
         <!-- Back -->
         <button
-          @click="$router.go(-1)"
+          @click="$router.back()"
           class="text-lg text-center px-2 py-1 absolute -left-2 -top-1"
         >
           <font-awesome icon="chevron-left" class="fa-fw"></font-awesome>