Backport PR #57490 on branch 2.2.x (DOC: Add a few deprecation notes) (#57509)

Backport PR #57490: DOC: Add a few deprecation notes

Co-authored-by: Patrick Hoefler <61934744+phofl@users.noreply.github.com>

Author: meeseeksmachine

pandas/core/dtypes/common.py

@@ -169,6 +169,9 @@ def is_sparse(arr) -> bool:
     """
     Check whether an array-like is a 1-D pandas sparse array.
 
+    .. deprecated:: 2.1.0
+        Use isinstance(dtype, pd.SparseDtype) instead.
+
     Check that the one-dimensional array-like is a pandas sparse array.
     Returns True if it is a pandas sparse array, not another type of
     sparse array.
@@ -295,6 +298,9 @@ def is_datetime64tz_dtype(arr_or_dtype) -> bool:
     """
     Check whether an array-like or dtype is of a DatetimeTZDtype dtype.
 
+    .. deprecated:: 2.1.0
+        Use isinstance(dtype, pd.DatetimeTZDtype) instead.
+
     Parameters
     ----------
     arr_or_dtype : array-like or dtype
@@ -381,6 +387,9 @@ def is_period_dtype(arr_or_dtype) -> bool:
     """
     Check whether an array-like or dtype is of the Period dtype.
 
+    .. deprecated:: 2.2.0
+        Use isinstance(dtype, pd.Period) instead.
+
     Parameters
     ----------
     arr_or_dtype : array-like or dtype
@@ -424,6 +433,9 @@ def is_interval_dtype(arr_or_dtype) -> bool:
     """
     Check whether an array-like or dtype is of the Interval dtype.
 
+    .. deprecated:: 2.2.0
+        Use isinstance(dtype, pd.IntervalDtype) instead.
+
     Parameters
     ----------
     arr_or_dtype : array-like or dtype
@@ -470,6 +482,9 @@ def is_categorical_dtype(arr_or_dtype) -> bool:
     """
     Check whether an array-like or dtype is of the Categorical dtype.
 
+    .. deprecated:: 2.2.0
+        Use isinstance(dtype, pd.CategoricalDtype) instead.
+
     Parameters
     ----------
     arr_or_dtype : array-like or dtype