feat(stable-sync): Move stable sync process within github tools

[alucardzom]

This PR consolidates duplicate script functionality from the Mobile and Extension repositories into our centralized GitHub tools repository. Instead of maintaining separate copies of similar scripts in each platform repository, both teams now reference a single, shared implementation via reusable workflows.

Key improvements

• Eliminates code duplication between Mobile and Extension platforms
• Provides a single source of truth for shared script logic
• Reduces maintenance overhead while maintaining existing functionality
• Follows our established pattern of centralizing common tooling

This change preserves all current processes and workflows while creating a more maintainable foundation for future updates.

See: https://github.com/MetaMask/MetaMask-planning/issues/4210

[cursor]

Bug: Incorrect Version Retrieval in Yarn Script

The extension-specific logic for yarn version incorrectly retrieves the package.json from origin/${baseBranch} instead of origin/main. This causes the script to apply an outdated version from the baseBranch (e.g., 'stable') instead of the latest version from main, which is necessary for a proper main-to-stable sync.

.github/scripts/stable-sync.js#L104-L107

github-tools/.github/scripts/stable-sync.js

Lines 104 to 107 in 6223ebd

	const { stdout: packageJsonContent } = await exec(
	`git show origin/${baseBranch}:package.json`,
	);

Fix in Cursor • Fix in Web

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[makemesteaks]

Should this also be stable instead of main?

[alucardzom]

Yeah that's why I've updated it and tested it again, to use the correct stable branch which is passed as an argument. Mobile uses the stable branch, extension uses master (once they align the branch naming, will be a matter of updating the GH Workflow input).

Thanks!!