[Xcode 26] Theme is not applied when system is dark mode

### Before submitting a new issue

- [x] I tested using the latest version of the library, as the bug might be already fixed.
- [x] I tested using a [supported version](https://github.com/reactwg/react-native-releases/blob/main/docs/support.md) of react native.
- [x] I checked for possible duplicate issues, with possible answers.

### Bug summary

Maybe related to: https://github.com/software-mansion/react-native-screens/issues/3162

On iOS, if we have DefaultTheme we can see that bottom bar is not applying the light theme but system theme instead

On this we can see that BottomBar style is updated with no reason :

https://github.com/user-attachments/assets/27375e07-425c-4866-acdb-8a4d301403fd

### Library version

0.10.1

### Environment info

```shell
Expo 53
RN 0.79
```

### Steps to reproduce

- Xcode 26 & iOS 26 (with dark theme on system)
- Launch app from the repo
- Open profile
- See that the bottom bar does not have the right theme

### Reproducible sample code

```js
https://github.com/huextrat/repro-screens-ios
```

Start with the linked reproducible sample and follow the listed steps on Xcode 26 and iOS 26 with the system in dark mode. Inspect why the BottomBar style changes when DefaultTheme is expected; done means the bottom bar keeps the correct light theme when the app launches from the profile screen.

Written by the indexing model from the issue text.