Initialize merge bot on all PRs upon installation

When installing the merge bot to a repository for the first time, it should initialize the check runs on all the open PRs.

Not high priority, since there’s a workaround

```
git commit --amend --date now -C HEAD
git push -f
```

Start by tracing the installation handling and the code that creates GitHub check runs for pull requests. Verify how open PRs are discovered during first-time installation, then confirm that every existing open PR receives its check runs without requiring the documented commit-amend workaround.

Written by the indexing model from the issue text.