BUG: Using pd.concat(axis="columns") on differently sized MultiIndexed DataFrames with a datetime index level containing exclusively NaT values causes the level in the returned DataFrame to be a float instead of a datetime

[Xnot]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• (optional) I have confirmed this bug exists on the master branch of pandas.

---

import pandas as pd

print(pd.__version__)
df_a = pd.DataFrame({"a": range(5), "idx1": range(5), "idx2": [pd.NaT] * 5}).set_index(["idx1", "idx2"])
df_b = pd.DataFrame({"b": range(6), "idx1": range(6), "idx2": [pd.NaT] * 6}).set_index(["idx1", "idx2"])
df = pd.concat([df_a, df_b], axis="columns")
df.reset_index().info()

On pandas 1.3.5:

1.3.5
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 6 entries, 0 to 5
Data columns (total 4 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   idx1    6 non-null      int64  
 1   idx2    0 non-null      float64
 2   a       5 non-null      float64
 3   b       6 non-null      int64  
dtypes: float64(2), int64(2)
memory usage: 320.0 bytes

On pandas 1.2.5:

1.2.5
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 6 entries, 0 to 5
Data columns (total 4 columns):
 #   Column  Non-Null Count  Dtype         
---  ------  --------------  -----         
 0   idx1    6 non-null      int64         
 1   idx2    0 non-null      datetime64[ns]
 2   a       5 non-null      float64       
 3   b       6 non-null      int64         
dtypes: datetime64[ns](1), float64(1), int64(2)
memory usage: 320.0 bytes

1.2.5 has the correct expected output. In 1.3.5, the datetime NaTs index has been converted to float NaNs. The bug only occurs if the DataFrames have different lengths and the index level in question contains only NaTs.

[simonjayhawkins]

1.2.5 has the correct expected output.

first bad commit: [0b671be] REF: unify casting logic in Categorical.init (#40097)