sage.rings: Remove code deprecated in #23204, #24483, #24371, #24511, #25848, #26105, #28481, #29010, #29412, #30332, #30372, #31345, #32375, #32606, #32610, #32612, #32641, #32660, #32750, #32869, #33602

[mkoeppe]

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[github-actions]

Documentation preview for this PR (built with commit 5cecd1c; changes) is ready! 🎉

[jhpalmieri]

Looks good, and all of these deprecations are old enough to be removed.

[mkoeppe]

Thank you!