[Paper] Update the paper Gallery app to 0.81.0-preview.6

[Copilot]

Description

Why

Update the paper Gallery app to react-native-windows 0.81.0-preview.6, following the pattern established in PR #571.

Resolves #577

What

• package.json - Version bumps:

  • react-native: 0.80.0 → 0.81.0-nightly-20250709-6892dde36 (matches react-native-windows peerDependency)
  • react-native-windows: 0.80.0 → 0.81.0-preview.6
  • @react-native/babel-preset, @react-native/eslint-config, @react-native/metro-config, @react-native/typescript-config: 0.80.0 → 0.81.0-nightly-20250709-6892dde36

• windows/rngallery/Package.appxmanifest - Incremented version: 2.0.0.0 → 2.0.1.0

• windows/rngallery/rngallery.vcxproj - Updated version comment to 0.81.0-preview.6

• yarn.lock - Regenerated with updated dependencies

Screenshots

N/A - Dependency version update only

Original prompt

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This section details on the original issue you should resolve

<issue_title>[Paper] Update the paper Gallery app to 0.81.0-preview.6</issue_title>
<issue_description>Refer this PR and update the paper app to 0.81.0-preview.6 https://github.com/microsoft/react-native-gallery/pull/571/files
You would need to update the package.json as listed in above PR.
The diff should be similar.

update minor version here windows/rngallery/Package.appxmanifest increment by 1

update comment in this file to point to latest current version windows/rngallery/rngallery.vcxproj</issue_description>

<agent_instructions>update the paper app to 0.81.0-preview.6 by referring the issue description</agent_instructions>

Comments on the Issue (you are @copilot in this section)

• Fixes [Paper] Update the paper Gallery app to 0.81.0-preview.6 #755

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