BUG: Infinite recursion with outer merge on categorical key column if left and right dtypes are mismatching non-nullable numeric kinds

[wence-]

Pandas version checks

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

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

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd
import numpy as np
lt = pd.CategoricalDtype(categories=np.asarray([1, 2, 3], dtype="int64"))
rt = pd.CategoricalDtype(categories=np.asarray([1, 2, 3], dtype="float64"))
left = pd.DataFrame({"key": pd.Series([1, 2], dtype=lt)})
right = pd.DataFrame({"key": pd.Series([1, 3], dtype=rt)})
left.merge(right, on="key", how="outer")

Issue Description

  [...]
  File "<stdin>", line 1, in <module>
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/frame.py", line 10737, in merge
    return merge(
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/reshape/merge.py", line 185, in merge
    return op.get_result(copy=copy)
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/reshape/merge.py", line 897, in get_result
    self._maybe_add_join_keys(result, left_indexer, right_indexer)
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/reshape/merge.py", line 1076, in _maybe_add_join_keys
    key_col = Index(lvals).where(~mask_left, rvals)
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/indexes/base.py", line 5237, in where
    return self.putmask(~cond, other)
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/indexes/base.py", line 5493, in putmask
    return self.astype(dtype).putmask(mask, value)
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/indexes/base.py", line 5493, in putmask
    return self.astype(dtype).putmask(mask, value)
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/indexes/base.py", line 5493, in putmask
    return self.astype(dtype).putmask(mask, value)
  [Previous line repeated 984 more times]
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/indexes/base.py", line 1057, in astype
    return self.copy() if copy else self
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/indexes/base.py", line 1259, in copy
    name = self._validate_names(name=name, deep=deep)[0]
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/indexes/base.py", line 1701, in _validate_names
    validate_all_hashable(*new_names, error_name=f"{type(self).__name__}.name")
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/dtypes/common.py", line 1575, in validate_all_hashable
    if not all(is_hashable(arg) for arg in args):
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/dtypes/common.py", line 1575, in <genexpr>
    if not all(is_hashable(arg) for arg in args):
  File "/home/wence/Documents/src/rapids/third-party/pandas/pandas/core/dtypes/inference.py", line 366, in is_hashable
    hash(obj)
RecursionError: maximum recursion depth exceeded while calling a Python object

Expected Behavior

I would expect this to complete, probably behaving as if the left and right key columns were of type int64 and float64. I would also accept raising.

Installed Versions

INSTALLED VERSIONS
------------------
commit                : b864b8eb54605124827e6af84aa7fbc816cfc1e0
python                : 3.10.12.final.0
python-bits           : 64
OS                    : Linux
OS-release            : 6.2.0-37-generic
Version               : #38~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Thu Nov  2 18:01:13 UTC 2
machine               : x86_64
processor             : x86_64
byteorder             : little
LC_ALL                : None
LANG                  : en_GB.UTF-8
LOCALE                : en_GB.UTF-8

pandas                : 2.1.0.dev0+1414.gb864b8eb54
numpy                 : 1.24.4
pytz                  : 2023.3
dateutil              : 2.8.2
setuptools            : 67.7.2
pip                   : 23.2.1
Cython                : 3.0.0
pytest                : 7.4.0
hypothesis            : 6.82.2
sphinx                : 6.2.1
blosc                 : None
feather               : None
xlsxwriter            : 3.1.2
lxml.etree            : 4.9.3
html5lib              : 1.1
pymysql               : 1.4.6
psycopg2              : 2.9.6
jinja2                : 3.1.2
IPython               : 8.14.0
pandas_datareader     : None
adbc-driver-postgresql: None
adbc-driver-sqlite    : None
bs4                   : 4.12.2
bottleneck            : 1.3.7
dataframe-api-compat  : None
fastparquet           : 2023.7.0
fsspec                : 2023.6.0
gcsfs                 : 2023.6.0
matplotlib            : 3.7.2
numba                 : 0.57.1
numexpr               : 2.8.4
odfpy                 : None
openpyxl              : 3.1.2
pandas_gbq            : None
pyarrow               : 12.0.1
pyreadstat            : 1.2.2
python-calamine       : None
pyxlsb                : 1.0.10
s3fs                  : 2023.6.0
scipy                 : 1.11.1
sqlalchemy            : 2.0.19
tables                : 3.8.0
tabulate              : 0.9.0
xarray                : 2023.7.0
xlrd                  : 2.0.1
zstandard             : 0.19.0
tzdata                : 2023.3
qtpy                  : 2.4.0
pyqt5                 : None

[rob-sil]

take

[rob-sil]

Looks like the same type of bug as #52927, just showing up in different places.