gh-37628: use the polynomial ring also for non-commutative baserings as _internal_poly_ring
    
The `LazyCompletionGradedAlgebra` used a univariate `FreeAlgebra` as
`_internal_poly_ring`, which doesn't work for 'exact' lazy series, i.e.,
when the degree is finite and all coefficients are known.

This was done, because it was assumed that there are issues with
univariate polynomials over a non-commutative base ring.  However, it
seems that these issues are not visible anymore.

Fixes #37625.
    
URL: #37628
Reported by: Martin Rubey
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/rings/lazy_series_ring.py

@@ -2716,6 +2716,13 @@ def __init__(self, basis, sparse=True, category=None):
             ...
             ValueError: basis should be in GradedAlgebrasWithBasis
 
+        Check that :issue:`37625` is fixed::
+
+            sage: R = algebras.Free(QQ, ('a', 'b'), degrees=(1, 2))
+            sage: L = R.completion()
+            sage: a, b = R.gens()
+            sage: (L(a) + L(b))^2
+            a^2 + (a*b+b*a) + b^2
         """
         base_ring = basis.base_ring()
         self._minimal_valuation = 0
@@ -2738,11 +2745,7 @@ def __init__(self, basis, sparse=True, category=None):
         Parent.__init__(self, base=base_ring, category=category)
         self._sparse = sparse
         self._laurent_poly_ring = basis
-        if self._laurent_poly_ring not in Rings().Commutative():
-            from sage.algebras.free_algebra import FreeAlgebra
-            self._internal_poly_ring = FreeAlgebra(self._laurent_poly_ring, 1, "DUMMY_VARIABLE")
-        else:
-            self._internal_poly_ring = PolynomialRing(self._laurent_poly_ring, "DUMMY_VARIABLE", sparse=sparse)
+        self._internal_poly_ring = PolynomialRing(self._laurent_poly_ring, "DUMMY_VARIABLE", sparse=sparse)
 
     def _repr_(self):
         """