BUG: melt method doesn't seem to preserve timezone settings.

[sasaki000]

Pandas version checks

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Reproducible Example

import pandas as pd

df = pd.DataFrame(data=[
    {'type': 'A0', 'start_date': pd.Timestamp('2023/03/01', tz='Asia/Tokyo'), 'end_date': pd.Timestamp('2023/03/10', tz='Asia/Tokyo')},
    {'type': 'A1', 'start_date': pd.Timestamp('2023/03/01', tz='Asia/Tokyo'), 'end_date': pd.Timestamp('2023/03/11', tz='Asia/Tokyo')},
], index=['aaaa', 'bbbb'])
display(df)

df = df.melt(id_vars=['type'], value_vars=['start_date', 'end_date'], var_name='start/end', value_name='date')
display(df)

Issue Description

The melt method doesn't seem to preserve timezone settings.

Expected Behavior

Even after executing the melt method, it is desirable that the time zone settings remain the same as before executing the melt method.

Installed Versions

Name: pandas
Version: 2.1.1
Summary: Powerful data structures for data analysis, time series, and statistics
Home-page: https://pandas.pydata.org/
Author:
Author-email: The Pandas Development Team pandas-dev@python.org
License: BSD 3-Clause License

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Location: /home/sasaki/workspace/orcas_proj/venv/lib/python3.10/site-packages
Requires: numpy, python-dateutil, pytz, tzdata
Required-by: bokeh, mplfinance, seaborn

[samukweku]

pivot_longer preserves the dtypes:

# pip install pyjanitor
import pandas as pd
import janitor

df.pivot_longer(index='type', names_to='start/end', values_to='date')

  type   start/end                      date
0   A0  start_date 2023-03-01 00:00:00+09:00
1   A1  start_date 2023-03-01 00:00:00+09:00
2   A0    end_date 2023-03-10 00:00:00+09:00
3   A1    end_date 2023-03-11 00:00:00+09:00

with respect to pd.melt, I suspect the issue lies in line 137 - the same logic applied to id_vars in line 125 should be replicated there as well. Not a bad idea @sasaki000 if you raise a PR for this