sagemathgh-39486: Finish changing Rational's round method default rounding to even
    
Follow-up to sagemath#35756 .

(As is, the warning cannot be suppressed)

Related: sagemath#37306,
sagemath#21935

There's a little (large??) problem: previously `K2.<sqrt2> =
QuadraticField(2); K2(9/2).round()` returns `5` **without** a warning
(because sagemath#35756 forget to print the deprecation). Should we add the
deprecation first **then** change this next year?

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

### ⌛ Dependencies

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URL: sagemath#39486
Reported by: user202729
Reviewer(s): Vincent Neiger

Author: Release Manager

src/sage/rings/number_field/number_field_element_quadratic.pyx

@@ -2382,8 +2382,6 @@ cdef class NumberFieldElement_quadratic(NumberFieldElement_absolute):
 
         TESTS::
 
-            sage: import warnings
-            sage: warnings.filterwarnings("ignore", category=DeprecationWarning)
             sage: K2.<sqrt2> = QuadraticField(2)
             sage: K3.<sqrt3> = QuadraticField(3)
             sage: K5.<sqrt5> = QuadraticField(5)
@@ -2398,15 +2396,15 @@ cdef class NumberFieldElement_quadratic(NumberFieldElement_absolute):
             ....:    assert round(a+b*sqrt(5.)) == round(a+b*sqrt5), (a, b)
         """
         n = self.floor()
-        test = 2 * (self - n).abs()
+        test = 2 * (self - n)
         if test < 1:
             return n
         elif test > 1:
             return n + 1
-        elif self > 0:
-            return n + 1
-        else:
+        elif n % 2 == 0:
             return n
+        else:
+            return n + 1
 
 
 cdef class NumberFieldElement_quadratic_sqrt(NumberFieldElement_quadratic):

src/sage/rings/rational.pyx

@@ -3375,11 +3375,9 @@ cdef class Rational(sage.structure.element.FieldElement):
         mpz_tdiv_q(n.value, mpq_numref(self.value), mpq_denref(self.value))
         return n
 
-    def round(Rational self, mode=None):
+    def round(Rational self, mode="even"):
         """
-        Return the nearest integer to ``self``, rounding away by default.
-        Deprecation: in the future the default will be changed to rounding to
-        even, for consistency with the builtin Python :func:`round`.
+        Return the nearest integer to ``self``, rounding to even by default.
 
         INPUT:
 
@@ -3399,15 +3397,13 @@ cdef class Rational(sage.structure.element.FieldElement):
         EXAMPLES::
 
             sage: (9/2).round()
-            doctest:...: DeprecationWarning: the default rounding for rationals, currently `away`, will be changed to `even`.
-            See https://github.com/sagemath/sage/issues/35473 for details.
-            5
+            4
             sage: n = 4/3; n.round()
             1
             sage: n = -17/4; n.round()
             -4
             sage: n = -5/2; n.round()
-            -3
+            -2
             sage: n.round("away")
             -3
             sage: n.round("up")
@@ -3419,12 +3415,6 @@ cdef class Rational(sage.structure.element.FieldElement):
             sage: n.round("odd")
             -3
         """
-        if mode is None:
-            if self.denominator() == 2:
-                from sage.misc.superseded import deprecation
-                deprecation(35473,
-                    "the default rounding for rationals, currently `away`, will be changed to `even`.")
-            mode = "away"
         if not (mode in ['toward', 'away', 'up', 'down', 'even', 'odd']):
             raise ValueError("rounding mode must be one of 'toward', 'away', 'up', 'down', 'even', or 'odd'")
         if self.denominator() == 1: