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/ImageMethodDialog.vue

@@ -41,7 +41,11 @@
                 @click="acceptUrl"
               />
               <!-- so that there's no shifting when it becomes visible -->
-              <font-awesome v-else icon="check" class="text-white bg-white px-2 py-2" />
+              <font-awesome
+                v-else
+                icon="check"
+                class="text-white bg-white px-2 py-2"
+              />
             </span>
           </div>
         </div>