gh-118692: Avoid creating unnecessary StopIteration instances for monitoring

[iritkatriel]

Fixes #118692.

• Issue: gh-118692

---

📚 Documentation preview 📚: https://cpython-previews--119216.org.readthedocs.build/

[bedevere-app[bot]]

When you're done making the requested changes, leave the comment: I have made the requested changes; please review again.

[iritkatriel]

I have made the requested changes; please review again.

[bedevere-app[bot]]

Thanks for making the requested changes!

@markshannon: please review the changes made to this pull request.

[scoder]

This needs backporting to 3.13.

[miss-islington-app[bot]]

Thanks @iritkatriel for the PR 🌮🎉.. I'm working now to backport this PR to: 3.13. 🐍🍒⛏🤖

[bedevere-app[bot]]

GH-119497 is a backport of this pull request to the 3.13 branch.