gh-35389: `sage.rings.finite_rings.residue_field`: Modularization fixes
    
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### 📚 Description
Splitting out the implementations that depend on libraries NTL, PARI,
Givaro to separate libraries.

Marking doctests `# optional`.

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This is part of:
- #29705

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### ⌛ Dependencies

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- Depends on #35283
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URL: #35389
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee

Author: Release Manager