gh-37611: Ensure degree and total degree return `Integer` type for `MPolynomial_polydict` class
    
This is a follow up PR to #37605
which ensures that `degree()` and `total_degree()` return a sage
`Integer` type instead of a python `int` for the `MPolynomial_polydict`
class.

However, `f.degrees()` returns something of type
`sage.rings.polynomial.polydict.ETuple` which has elements as `int`. I
am loathed to change this to return `Integer` in case of performance
regression, so the following status of `MPolynomial_polydict` is the
following:

```py
sage: R.<x, y> = PolynomialRing(QQbar)
sage: f = 1 + x + y^2
sage: type(f.degree())
<class 'sage.rings.integer.Integer'>
sage: type(f.degree(x))
<class 'sage.rings.integer.Integer'>
sage: type(f.degree(y))
<class 'sage.rings.integer.Integer'>
sage: type(f.total_degree())
<class 'sage.rings.integer.Integer'>
sage: type(f.degrees())
<class 'sage.rings.polynomial.polydict.ETuple'>
sage: type(f.degrees()[0])
<class 'int'>
```

I would like advice on how to proceed with the `degrees()` function. Is
leaving it in it's current state OK?

Fixes #37603
    
URL: #37611
Reported by: Giacomo Pope
Reviewer(s): Giacomo Pope, grhkm21

Author: Release Manager

src/sage/rings/polynomial/multi_polynomial_element.py

@@ -668,10 +668,21 @@ def degree(self, x=None, std_grading=False):
             sage: R.<x,y> = GF(3037000453)[]                                            # needs sage.rings.finite_rings
             sage: R.zero().degree(x)
             -1
+
+        Ensure that :issue:`37603` is fixed::
+
+            sage: R.<x,y,z> = PolynomialRing(QQbar)
+            sage: f = 3*x^2 - 2*y + 7*x^2*y^2 + 5
+            sage: type(f.degree())
+            <class 'sage.rings.integer.Integer'>
+            sage: type(f.degree(x))
+            <class 'sage.rings.integer.Integer'>
+            sage: type(f.degree(x)) == type(f.degree(y)) == type(f.degree(z))
+            True
         """
         if x is None:
             if std_grading or not self.parent().term_order().is_weighted_degree_order():
-                return self.element().degree(None)
+                return Integer(self.element().degree(None))
             return self.weighted_degree(self.parent().term_order().weights())
         if isinstance(x, MPolynomial):
             if not x.parent() is self.parent():
@@ -683,7 +694,7 @@ def degree(self, x=None, std_grading=False):
                 raise TypeError("x must be one of the generators of the parent")
         else:
             raise TypeError("x must be one of the generators of the parent")
-        return self.element().degree(x.element())
+        return Integer(self.element().degree(x.element()))
 
     def total_degree(self):
         """
@@ -712,6 +723,16 @@ def total_degree(self):
             sage: f = z^9 + 10*x^4 + y^8*x^2
             sage: f.total_degree()
             10
+
+        TESTS:
+
+        Ensure that :issue:`37603` is fixed::
+             sage: R.<x,y,z> = QQbar[]
+             sage: f = 2*x*y^3*z^2
+             sage: f.total_degree()
+             6
+             sage: type(f.total_degree())
+             <class 'sage.rings.integer.Integer'>
         """
         return self.degree()