gh-37651: use parent in asymptotic ring
trying to use the modern `Parent` and categories in the asymptotic ring,
instead of the auld `Algebra`
### :memo: Checklist
- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
URL: https://github.com/sagemath/sage/pull/37651
Reported by: Frédéric Chapoton
Reviewer(s): Marc Mezzarobba
