sync reports success (exit 0) when its internal push fails

(This issue was AI generated but I have read it, understood it, and I'm accountable for its content.)

**Version**: gh-stack v0.1.0.

**Repro**: a stack whose branches are already pushed; rebase the stack locally (tips now require a force-push); run `gh stack sync`.

**Actual output**:

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

with **exit code 0**, while the branches were not pushed.

**Expected**: either sync pushes with `--force-with-lease --atomic` as its own documentation describes (step 5 of the sync help text), or the run exits non-zero when the push step fails. A warning followed by a success line and a zero exit makes sync unusable in scripts and easy to misread interactively.

Start at the `gh stack sync` command and trace how the internal push result is handled after a rebased stack requires a force push. Reproduce the reported scenario, then verify that a failed push cannot produce a successful sync result or exit code; add or update a regression test if the surrounding command tests provide one.

Written by the indexing model from the issue text.