DOC: fix PR07,SA01 for pandas.MultiIndex.sortlevel (#59521)

ci/code_checks.sh

@@ -72,7 +72,6 @@ if [[ -z "$CHECK" || "$CHECK" == "docstrings" ]]; then
         -i "pandas.Series.dt PR01" `# Accessors are implemented as classes, but we do not document the Parameters section` \
         -i "pandas.MultiIndex.names SA01" \
         -i "pandas.MultiIndex.reorder_levels RT03,SA01" \
-        -i "pandas.MultiIndex.sortlevel PR07,SA01" \
         -i "pandas.MultiIndex.to_frame RT03" \
         -i "pandas.NA SA01" \
         -i "pandas.NaT SA01" \

pandas/core/indexes/multi.py

@@ -2681,8 +2681,15 @@ def sortlevel(
         """
         Sort MultiIndex at the requested level.
 
-        The result will respect the original ordering of the associated
-        factor at that level.
+        This method is useful when dealing with MultiIndex objects, allowing for
+        sorting at a specific level of the index. The function preserves the
+        relative ordering of data within the same level while sorting
+        the overall MultiIndex. The method provides flexibility with the `ascending`
+        parameter to define the sort order and with the `sort_remaining` parameter to
+        control whether the remaining levels should also be sorted. Sorting a
+        MultiIndex can be crucial when performing operations that require ordered
+        indices, such as grouping or merging datasets. The `na_position` argument is
+        important in handling missing values consistently across different levels.
 
         Parameters
         ----------
@@ -2692,7 +2699,9 @@ def sortlevel(
         ascending : bool, default True
             False to sort in descending order.
             Can also be a list to specify a directed ordering.
-        sort_remaining : sort by the remaining levels after level
+        sort_remaining : bool, default True
+            If True, sorts by the remaining levels after sorting by the specified
+            `level`.
         na_position : {'first' or 'last'}, default 'first'
             Argument 'first' puts NaNs at the beginning, 'last' puts NaNs at
             the end.
@@ -2706,6 +2715,13 @@ def sortlevel(
         indexer : np.ndarray[np.intp]
             Indices of output values in original index.
 
+        See Also
+        --------
+        MultiIndex : A multi-level, or hierarchical, index object for pandas objects.
+        Index.sort_values : Sort Index values.
+        DataFrame.sort_index : Sort DataFrame by the index.
+        Series.sort_index : Sort Series by the index.
+
         Examples
         --------
         >>> mi = pd.MultiIndex.from_arrays([[0, 0], [2, 1]])