gh stack sync reports success after its atomic push fails

## Reproduction

Start with an existing three-PR stack whose local branches were rebased and therefore require force pushes, then run:

```console
$ gh stack sync --remote origin
✓ Fetched latest dev from origin
✓ Trunk dev is already up to date

Pushing 3 branches to origin...
⚠ Push failed — branches may need force push after rebase
Run `gh stack push` to push with --force-with-lease.

Syncing PRs ...
✓ PR #4440 (...) — Open
✓ PR #4441 (...) — Open
✓ PR #4444 (...) — Open
⚠ Cannot create stack: Pull requests must form a stack, where each PR's base ref is the previous PR's head ref
Each PR's base branch must match the previous PR's head branch.

✓ Branches synced
Stacked on dev (a80f5ad)

$ echo $?
0
```

All three remote branch SHAs remained unchanged. The local stack was therefore not published, but `sync` continued into PR synchronization, printed a success receipt, and exited zero.

## Expected

`gh stack sync` exits nonzero immediately when its atomic branch push fails. It does not attempt PR synchronization or print `Branches synced`, because the remote stack cannot match local state until the branch refs are updated.

## Environment

- `gh-stack` v0.1.0
- `gh` 2.96.0
- git 2.50.1
- macOS arm64

## Related

#346 covers suppressed git-hook output during `gh stack push`. This report is about `sync` swallowing the failed-push status and returning a false success.

Start at the `gh stack sync` command and trace the atomic branch push result. Verify that a failed push stops PR synchronization, avoids the `Branches synced` receipt, and returns nonzero; add or update coverage for the reproduced three-PR rebase case.

Written by the indexing model from the issue text.