gh-36943: some details in multi_polynomial base
a few minor details in the modified file
mainly to use `Parent` in some place in the doc
### :memo: Checklist
- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation accordingly.
URL: https://github.com/sagemath/sage/pull/36943
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe
