fix(caret): prevent misalignment on initial load and resize (@byseif21, @nadalaba) (monkeytypegame#6641)

### Description

This PR fixes two related caret positioning issues that occurred
**before any user input**:

* **Resize Bug**:
Resizing the browser immediately after a page refresh caused the caret
to appear misaligned. The position only corrected itself after the user
typed the first character.

* **Navigation Bug**:
Navigating away from the test page and back (especially after a refresh)
caused the caret to initially render in the wrong position, then animate
into place.

---

### Solution

* Refactor `Caret.updatePosition()` to use `getComputedStyle` for
width/height instead of `getBoundingClientRect()` and `offsetHeight`
makes caret positioning more accurate.
* Redundant calls to Caret.updatePosition() have been removed from the
resize handler, relying instead on the more
 comprehensive caret re-initialization.


These changes resolve caret alignment and animation issues after
loading, resizing, or navigating, including in tape mode.

 
---

> ~~Replaced early calls to `Caret.updatePosition()` with `Caret.show()`
when no input has been entered yet.~~

>  ~~`Caret.show()` ensures the caret is:~~

> ~~* Visible~~
>  ~~* Properly initialized~~
>  ~~* Animated via `startAnimation()`~~
> ~~* Positioned correctly via internal `updatePosition()` call~~

> ~~Once the caret is initialized (i.e., after first input), we continue
using `updatePosition()` directly for subsequent updates.~~
>  

---

Closes monkeytypegame#6639

Author: byseif21

frontend/src/ts/test/caret.ts

@@ -133,9 +133,9 @@ function getTargetPositionLeft(
 }
 
 export async function updatePosition(noAnim = false): Promise<void> {
-  const caretWidth = Math.round(
-    document.querySelector("#caret")?.getBoundingClientRect().width ?? 0
-  );
+  const caretComputedStyle = window.getComputedStyle(caret);
+  const caretWidth = parseInt(caretComputedStyle.width) || 0;
+  const caretHeight = parseInt(caretComputedStyle.height) || 0;
 
   const fullWidthCaret = ["block", "outline", "underline"].includes(
     Config.caretStyle
@@ -170,10 +170,10 @@ export async function updatePosition(noAnim = false): Promise<void> {
 
   const letterPosTop =
     currentLetter?.offsetTop ?? lastWordLetter?.offsetTop ?? 0;
-  const diff = letterHeight - caret.offsetHeight;
+  const diff = letterHeight - caretHeight;
   let newTop = activeWordEl.offsetTop + letterPosTop + diff / 2;
   if (Config.caretStyle === "underline") {
-    newTop = activeWordEl.offsetTop + letterPosTop - caret.offsetHeight / 2;
+    newTop = activeWordEl.offsetTop + letterPosTop - caretHeight / 2;
   }
 
   let letterWidth = currentLetter?.offsetWidth;

frontend/src/ts/ui.ts

@@ -92,7 +92,6 @@ window.addEventListener("beforeunload", (event) => {
 });
 
 const debouncedEvent = debounce(250, () => {
-  void Caret.updatePosition();
   if (getActivePage() === "test" && !TestUI.resultVisible) {
     if (Config.tapeMode !== "off") {
       void TestUI.scrollTape();
@@ -102,7 +101,7 @@ const debouncedEvent = debounce(250, () => {
     setTimeout(() => {
       void TestUI.updateWordsInputPosition();
       if ($("#wordsInput").is(":focus")) {
-        Caret.show();
+        Caret.show(true);
       }
     }, 250);
   }