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/GiftedPrompts.vue

@@ -82,6 +82,7 @@ import { GiverReceiverInputInfo } from "../libs/util";
 @Component
 export default class GivenPrompts extends Vue {
   $notify!: (notification: NotificationIface, timeout?: number) => void;
+  $router!: Router;
 
   CATEGORY_CONTACTS = 1;
   CATEGORY_IDEAS = 0;
@@ -145,7 +146,7 @@ export default class GivenPrompts extends Vue {
     // proceed with logic but don't change values (just in case some actions are added later)
     this.visible = false;
     if (this.currentCategory === this.CATEGORY_IDEAS) {
-      (this.$router as Router).push({
+      this.$router.push({
         name: "contact-gift",
         query: {
           prompt: this.IDEAS[this.currentIdeaIndex],