BUG: Fix replacing in string series with NA (pandas-dev#32621)

Made improvements based on the tests which failed

Author: chrispe

pandas/core/internals/managers.py

@@ -1936,11 +1936,18 @@ def _compare_or_regex_search(a, b, regex=False):
     is_a_array = isinstance(a, np.ndarray)
     is_b_array = isinstance(b, np.ndarray)
 
+    def _get_nan_value(x):
+        if np.issubdtype(x.dtype, np.datetime64):
+            return np.datetime64('NaT')
+        elif np.issubdtype(x.dtype, np.timedelta64):
+            return np.timedelta64('NaT')
+        return np.nan
+
     # Replace all definitions of missing values (isna=True) to a numpy.nan
     if is_a_array:
-        a = np.where(isna(a), np.nan, a)
+        a = np.where(isna(a), _get_nan_value(a), a)
     if is_b_array:
-        b = np.where(isna(b), np.nan, b)
+        b = np.where(isna(b), _get_nan_value(b), b)
 
     if is_datetimelike_v_numeric(a, b) or is_numeric_v_string_like(a, b):
         # GH#29553 avoid deprecation warnings from numpy