Rotating the screen with the set due date dialog open resets the study screen

### Checked for duplicates?

- [x] This issue is not a duplicate

### Does it also happen in the desktop version?

- [x] This bug does not occur in the latest version of Anki Desktop

### What are the steps to reproduce this bug?

Add some code to the template to make it random, for example:

```html

var e = document.getElementById('t');
e.innerHTML = Math.random();

```

then open the set due date dialog and rotate the screen. Notice that the screen was reset, so the number is different.

https://github.com/user-attachments/assets/e3335ad0-e863-4610-bdf9-4f7aa10ec2f5

### Expected behaviour

No resetting.

### Debug info

```text
AnkiDroid Version = 2.24.0alpha14 (b9e52b175cd656018d0655da8ddcfb37ed10b881)
Backend Version = 0.1.64-anki25.09.2 (25.09.2 3890e12c9e48c028c3f12aa58cb64bd9f8895e30)
Android Version = 13 (SDK 33)
ProductFlavor = full
Device Info = Xiaomi | POCO | mondrian | mondrian_global | 23013PC75G | qcom
WebView Info = [com.google.android.webview | 768017703]: Mozilla/5.0 (Linux; Android 13; 23013PC75G Build/TKQ1.220905.001; wv) AppleWebKit/537.36 (KHTML, like Gecko) Version/4.0 Chrome/146.0.7680.177 Mobile Safari/537.36
ACRA UUID = 4afc3b3f-e93f-4a66-bc71-2b9476ef9eb0
FSRS = 5.1.0 (Enabled: true)
Crash Reports Enabled = true
```

### (Optional) Anything else you want to share?

Also happens in the old study screen and in the new beta.

### Research

- [x] I have checked the [manual](https://ankidroid.org/docs/manual.html) and the [FAQ](https://github.com/ankidroid/Anki-Android/wiki/FAQ) and could not find a solution to my issue
- [x] (Optional) I have confirmed the issue is not resolved in the latest alpha release ([instructions](https://docs.ankidroid.org/manual.html#betaTesting))