DOC: Add a few deprecation notes (pandas-dev#57490)

* DOC: Add a few deprecation notes

* Update common.py

* Update common.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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---------

Co-authored-by: Thomas Li <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: 3 people

pandas/core/dtypes/common.py

@@ -168,6 +168,9 @@ 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.
@@ -294,6 +297,9 @@ 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
@@ -380,6 +386,9 @@ 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
@@ -423,6 +432,9 @@ 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
@@ -469,6 +481,9 @@ 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