gh-37133: use Parent in free_algebra_quotient
change to use `Parent` in the modified file
a little step towards removal the old coercion framework
also making a little refreshing for doc and pep8
### :memo: Checklist
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URL: https://github.com/sagemath/sage/pull/37133
Reported by: Frédéric Chapoton
Reviewer(s): Travis Scrimshaw