Fix PR preview responder setting correct origin remote (#2528)

#skip-bb
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<!-- This is an auto-generated description by cubic. -->
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## Summary by cubic
Fixes the PR review responder so pushes go to the PR’s fork instead of
the base repo on forked PRs. Exposes the head repository and sets
origin’s pushurl to ensure correct push behavior.

- **Bug Fixes**
- Exposes head_repo from workflow_run (run.head_repository.full_name)
for later steps.
- Adds a step to set origin’s pushurl to the PR’s head repo using
GITHUB_TOKEN, preventing accidental pushes to the base repo after
claude-code-action rewrites origin.

<sup>Written for commit 9ca4297.
Summary will update on new commits.</sup>

<!-- End of auto-generated description by cubic. -->

Co-authored-by: Will Chen <[email protected]>

Author: wwwillchen-bot

.github/workflows/pr-review-responder.yml

@@ -151,6 +151,7 @@ jobs:
             core.setOutput('should_continue', 'true');
             core.setOutput('request_count', requestCount);
             core.setOutput('current_label', currentLabel);
+            core.setOutput('head_repo', run.head_repository.full_name);
 
       - name: Checkout repository
         if: steps.pr-info.outputs.should_continue == 'true'
@@ -169,6 +170,18 @@ jobs:
         id: before-claude
         run: echo "sha=$(git rev-parse HEAD)" >> $GITHUB_OUTPUT
 
+      - name: Configure push remote for fork PRs
+        if: steps.pr-info.outputs.should_continue == 'true'
+        run: |
+          # claude-code-action overwrites origin's fetch URL to point to dyad-sh/dyad
+          # (using GITHUB_REPOSITORY which is always the base repo in workflow_run events).
+          # Setting pushurl separately ensures git push still targets the fork,
+          # because git uses pushurl over url when both are configured.
+          git remote set-url --push origin "https://x-access-token:${GITHUB_TOKEN}@github.com/${{ steps.pr-info.outputs.head_repo }}.git"
+          echo "Configured pushurl to ${{ steps.pr-info.outputs.head_repo }}"
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+
       - name: Update labels to pending
         if: steps.pr-info.outputs.should_continue == 'true'
         run: |