BUG: df.plot.box does not handle well when matplotlib Axes uses sharey=True

[glemaitre]

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Reproducible Example

This is a similar issue to #36918 that has been fixed for df.boxplot. But the issue remains for df.plot.box:

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

rng = np.random.default_rng(0)
df1 = pd.DataFrame(
    rng.integers(0, 100, size=(100, 4)), columns=list('ABCD')
)
df2 = pd.DataFrame(
    rng.integers(0, 100, size=(100, 4)), columns=list('ABCD')
)

f, axs = plt.subplots(1, 2, figsize=(10, 7), sharey=True)
df1.plot.box(ax=axs[0], showfliers=False, vert=False)
df2.plot.box(ax=axs[1], showfliers=False, vert=False)

Issue Description

The current code raise an error:

ValueError: The number of FixedLocator locations (8), usually from a call to set_ticks, does not match the number of ticklabels (4).

Expected Behavior

No errors

Installed Versions

INSTALLED VERSIONS
------------------
commit              : 9994adcfa12064ec0eb535786c43a93ec6aff15f
python              : 3.10.12.final.0
python-bits         : 64
OS                  : Darwin
OS-release          : 22.6.0
Version             : Darwin Kernel Version 22.6.0: Wed Jul  5 22:22:52 PDT 2023; root:xnu-8796.141.3~6/RELEASE_ARM64_T8103
machine             : arm64
processor           : arm
byteorder           : little
LC_ALL              : None
LANG                : en_US.UTF-8
LOCALE              : None.UTF-8

pandas              : 2.2.0dev0+164.g9994adcfa1
numpy               : 1.24.4
pytz                : 2023.3
dateutil            : 2.8.2
setuptools          : 68.1.2
pip                 : 23.2.1
Cython              : 0.29.33
pytest              : 7.4.0
hypothesis          : 6.83.0
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             : 8.15.0
pandas_datareader   : 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             : 13.0.0
pyreadstat          : 1.2.3
pyxlsb              : 1.0.10
s3fs                : 2023.6.0
scipy               : 1.11.2
sqlalchemy          : 2.0.20
tables              : 3.8.0
tabulate            : 0.9.0
xarray              : 2023.8.0
xlrd                : 2.0.1
zstandard           : 0.19.0
tzdata              : 2023.3
qtpy                : None
pyqt5               : None