REF: Enhance consistency on Styler methods (#45780)

* Enhance consistency on Styler hide methods

* Docs and checks

* Make set_sticky consistent with all other methods

* Remove whatsnew

* Apply suggestions from code review

Co-authored-by: JHM Darbyshire <24256554+attack68@users.noreply.github.com>

Co-authored-by: JHM Darbyshire <24256554+attack68@users.noreply.github.com>

Author: staticdev

pandas/io/formats/style.py

@@ -2598,11 +2598,11 @@ def hide_index(
         Styler.hide: Hide the entire index / columns, or specific rows / columns.
         """
         warnings.warn(
-            "this method is deprecated in favour of `Styler.hide(axis='index')`",
+            'this method is deprecated in favour of `Styler.hide(axis="index")`',
             FutureWarning,
             stacklevel=find_stack_level(),
         )
-        return self.hide(axis=0, level=level, subset=subset, names=names)
+        return self.hide(axis="index", level=level, subset=subset, names=names)
 
     def hide_columns(
         self,
@@ -2651,11 +2651,11 @@ def hide_columns(
         Styler.hide: Hide the entire index / columns, or specific rows / columns.
         """
         warnings.warn(
-            "this method is deprecated in favour of `Styler.hide(axis='columns')`",
+            'this method is deprecated in favour of `Styler.hide(axis="columns")`',
             FutureWarning,
             stacklevel=find_stack_level(),
         )
-        return self.hide(axis=1, level=level, subset=subset, names=names)
+        return self.hide(axis="columns", level=level, subset=subset, names=names)
 
     def hide(
         self,