Action cannot match an existing same-repository sync PR

Expected Behavior

When frog/sync already has an open pull request, the Action finds and updates that pull request.

Current Behavior

The Action requests headRepository and headRepositoryOwner from gh pr list, then compares .headRepository.nameWithOwner with the full repository name.

The GitHub CLI exposes .headRepository.name, but nameWithOwner is an empty string in this response. The comparison rejects the existing pull request. Later steps can then treat the pull request as absent.

Possible Solution

Compare both fields that the CLI populates:

.headRepositoryOwner.login == $owner and
.headRepository.name == $name

Derive $owner and $name separately from GITHUB_REPOSITORY.

Minimal Reproducible Example

For a repository with an open pull request, run:

gh pr list \
    --head frog/sync \
    --state open \
    --json number,headRepository,headRepositoryOwner

The repository object has this shape:

{
  "headRepository": {
    "name": "repo",
    "nameWithOwner": ""
  },
  "headRepositoryOwner": {
    "login": "owner"
  }
}

The current nameWithOwner == "owner/repo" condition is therefore false.

Context

The affected comparison is in action/action.yml at commit 702c4eadefe175a208290a99c36e7f4ac1390e53.

Inspect the affected comparison in action/action.yml at commit 702c4eadefe175a208290a99c36e7f4ac1390e53, then run the documented gh pr list command to confirm the response fields. Update the repository matching to use the owner login and repository name separately, and verify that an existing open frog/sync pull request is found rather than treated as absent.