sagemathgh-39365: Allow coercion from Frac(QQ[x]) to LaurentSeriesRing(QQ)
    
If `A` is a field then `self = LaurentSeriesRing(A)` is a field, by
universal property of fraction field, a coercion `P.base() → self` can
be uniquely extended to `P → self`. So this makes sense.

As a side effect, this coercion allows the user to write things such as

```sage
sage: R.<x> = QQ[]
sage: 1/(x-1)+O(x^100)
-1 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 - x^10 - x^11 -
x^12 - x^13 - x^14 - x^15 - x^16 - x^17 - x^18 - x^19 + O(x^20)
```

Another side effect: If the base ring is something like `Zmod(5)` or
`QQ["x"].quotient(...)` then a primality/irreducibility check will be
carried out.

### 📝 Checklist

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- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: sagemath#39365
Reported by: user202729
Reviewer(s):

Author: Release Manager

src/sage/rings/laurent_series_ring.py

@@ -676,6 +676,8 @@ def _coerce_map_from_(self, P):
             True
             sage: S.has_coerce_map_from(PolynomialRing(ZZ, 't'))
             True
+            sage: S.has_coerce_map_from(Frac(PolynomialRing(ZZ, 't')))
+            False
             sage: S.has_coerce_map_from(LaurentPolynomialRing(ZZ, 't'))
             True
             sage: S.has_coerce_map_from(PowerSeriesRing(ZZ, 't'))
@@ -698,6 +700,12 @@ def _coerce_map_from_(self, P):
             sage: S.has_coerce_map_from(LaurentSeriesRing(QQ, 't'))
             False
 
+            sage: T.<t> = LaurentSeriesRing(QQ)
+            sage: T.has_coerce_map_from(QQ['t'])
+            True
+            sage: T.has_coerce_map_from(Frac(QQ['t']))
+            True
+
             sage: R.<t> = LaurentSeriesRing(QQ['x'])
             sage: R.has_coerce_map_from(QQ[['t']])
             True
@@ -714,7 +722,10 @@ def _coerce_map_from_(self, P):
             sage: R.has_coerce_map_from(LazyLaurentSeriesRing(ZZ['x'], 't'))
             True
         """
+        from sage.rings.fraction_field import FractionField_generic
         A = self.base_ring()
+        if isinstance(P, FractionField_generic) and A.is_field():
+            return self.has_coerce_map_from(P.base())
         if (isinstance(P, (LaurentSeriesRing, LazyLaurentSeriesRing,
                            LaurentPolynomialRing_generic,
                            PowerSeriesRing_generic, LazyPowerSeriesRing,