Replace forked mobile editor dependencies

[dcalhoun]

This issues tracks various tasks for removing forked, third-party dependencies for the native mobile editor. The following tasks could likely be addressed individually as miniature projects.

What problem does this address?

The forked dependencies have caused issues in the past, e.g. #33424, #40540. We have adapted our approach to work around these issues, but the forked dependencies remain an inefficiency.

Current State

Dependency	Modify iOS	Modify Android	Modify Javascript	Removal Difficulty
react-native-reanimated	✅1			Low
react-native-prompt-android		✅		High
react-native-video		✅	✅	High
react-native-slider	✅		✅	Low
react-native-hsv-color-picker			✅~	Medium

What is your proposed solution?

We could remove dependency on the forked dependencies by committing fixes/required changes to the upstream repositories or internalizing the dependency in the form of implementing the dependency in the Gutenberg code directly.

• Replace react-native-reanimated forked repository.
• Replace react-native-prompt-android forked repository.
• Replace react-native-video forked repository.
• Upgrade to @react-native-community/slider@4.x and replace forked repository.
• Remove third-party dependency on react-native-hsv-color-picker wordpress-mobile/gutenberg-mobile#5847

Footnotes

1. The modification is made to Podfile to fix an actual issue from the upstream repository. ↩

[dcalhoun]

Noting that react-native-prompt-android was removed in #54096.