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/components/PushNotificationPermission.vue

@@ -69,7 +69,9 @@
                   class="rounded-r border border-slate-400 bg-slate-200 text-center text-blue-500 mt-2 px-2 py-2 w-20"
                   @click="hourAm = !hourAm"
                 >
-                  <span v-if="hourAm"> AM <font-awesome icon="chevron-down" /> </span>
+                  <span v-if="hourAm">
+                    AM <font-awesome icon="chevron-down" />
+                  </span>
                   <span v-else> PM <font-awesome icon="chevron-up" /> </span>
                 </span>
               </span>