gh-35230: `sage.rings.function_field`: Modularization fixes
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### 📚 Description
- We split out `.derivations` (which uses modules) from `.maps` (which
doesn't).
- We separate the implementation of rational function fields (which do
not need Singular for Gröbner basis calculations) from the
implementation of more complicated function fields (which do).
- We move some imports into methods.
This is for modularization purposes:
- Part of #29705
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### ⌛ Dependencies
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- Depends on #35237 (for the feature `sage.libs.singular`)
- Depends on #35119 (to preempt merge conflicts)
URL: https://github.com/sagemath/sage/pull/35230
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe
