Add conflict resolution extension point for PR backport workflow

[lbussell]

Part of dotnet/dotnet-docker#6653.

Background

We want automated backports in dotnet/dotnet-docker, but the repo has hundreds of checked-in files that are generated from templates. The templates often have different output depending on the branch. This means backports frequently create merge conflicts. Regenerating all of the templated files resolves most merge conflicts.

Changes

This PR adds an input to the backport workflow base that lets consuming workflows pass in a command that can be run to try and resolve merge conflicts. If there's a merge conflict, we run the custom conflict resolution command. If all of the merge conflicts/markers are resolved after the command is run, then we proceed with the pull request.

• Example of success:
  • Original PR: This change should cause a merge conflict lbussell/dotnet-docker#8 (comment)
  • Auto-generated PR: [main] This change should cause a merge conflict lbussell/dotnet-docker#11
    • Of note here is that it added all modified files even if they didn't exist in the target branch, even though that's technically incorrect for this scenario. That this is by-design. If we wanted to fix this, we would make the dotnet-docker repo's template generation scripts delete the extra files.
• Example of failure: This PR should cause an error when backported lbussell/dotnet-docker#6 (comment)

[lbussell]

/cc @nagilson for a review of the JavaScript.

[Copilot]

Pull Request Overview

This PR adds an automated conflict resolution mechanism to the backport workflow, allowing consuming repos to specify a custom command that attempts to resolve merge conflicts during automated backports.

Key changes:

• Adds a conflict_resolution_command input parameter that accepts a shell command to run when merge conflicts occur
• Implements conflict detection and resolution flow that stages changes, verifies conflicts are resolved, and continues the git am process
• Refactors error handling to use helper functions with improved GitHub comment formatting

[lbussell]

Ready for review again - updated the links to the examples as well.

[nagilson]

I think you mentioned this is not complete yet, but here are the thoughts I had so far.

[nagilson]

Looked over it again - the JS looks good to me from what I saw, though I left some feedback. Definitely in favor of this idea! :)