Fix custom screen swipe transitions

[piaskowyk]

Description

This PR fixes custom swipe-back transitions. The issue arose because, in the new version of React Native, they changed the way to obtain the shadow node wrapper. Since the ref to the screen is a native ref and we only need this on Fabric, it was possible to simplify the way we obtain that reference. Additionally, I found a small issue with the propagation of the ref and fixed it in the Screen implementation.

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	Screen.Recording.2025-09-25.at.13.22.20.mov

Example: https://github.com/software-mansion/react-native-reanimated/blob/main/apps/common-app/src/apps/reanimated/examples/ScreenTransitionExample.tsx

Checklist

• Included code example that can be used to test this change
• Updated TS types
• Updated documentation:
  • https://github.com/software-mansion/react-native-screens/blob/main/guides/GUIDE_FOR_LIBRARY_AUTHORS.md
  • https://github.com/software-mansion/react-native-screens/blob/main/native-stack/README.md
  • https://github.com/software-mansion/react-native-screens/blob/main/src/types.tsx
  • https://github.com/software-mansion/react-native-screens/blob/main/src/native-stack/types.tsx
• Ensured that CI passes

[kkafar]

Code changes look good. Thank you!

[kkafar]

I guess our definitions were already outdated, but will it work with 80, 81 & 82 now?

[piaskowyk]

I haven't tested it with all of these versions (only with 0.81), but to my knowledge, it should work with all of them.

[kkafar]

I'll merge it once I get to test this (soon)