refactor: replace jquery with dom utils in scroll-to-top button (@MoushufAlam) (monkeytypegame#7257)

### Description

Replaces jQuery usage with dom utils in the scroll-to-top button.
Scope intentionally kept small per contributing guidelines.

### Checks

- [x] Adding/modifying Typescript code?
  - [x] I have used `qs`, `qsa` or `qsr` instead of JQuery selectors.
- [x] Check if any open issues are related to this PR; if so, be sure to
tag them below.
- [x] Make sure the PR title follows the Conventional Commits standard.
(https://www.conventionalcommits.org for more info)
- [x] Make sure to include your GitHub username prefixed with @ inside
parentheses at the end of the PR title.

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Related to monkeytypegame#7186

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Author: MoushufAlam

frontend/src/ts/elements/scroll-to-top.ts

@@ -1,27 +1,30 @@
 import * as ActivePage from "../states/active-page";
 import { prefersReducedMotion } from "../utils/misc";
+import { qsr } from "../utils/dom";
 
 let visible = false;
 
+const button = qsr(".scrollToTopButton");
+
 export function hide(): void {
-  $(".scrollToTopButton").addClass("invisible");
+  button.addClass("invisible");
   visible = false;
 }
 
 function show(): void {
-  $(".scrollToTopButton").removeClass("invisible");
+  button.removeClass("invisible");
   visible = true;
 }
 
-$(document).on("click", ".scrollToTopButton", () => {
-  $(".scrollToTopButton").addClass("invisible");
+button.on("click", () => {
+  button.addClass("invisible");
   window.scrollTo({
     top: 0,
     behavior: prefersReducedMotion() ? "instant" : "smooth",
   });
 });
 
-$(window).on("scroll", () => {
+window.addEventListener("scroll", () => {
   const page = ActivePage.get();
   if (page === "test") return;