Pandas version checks

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

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Reproducible Example

from IPython.display import display, HTML

import numpy as np
import pandas as pd

df = pd.DataFrame(np.random.random((2,3)))
display(df)  # this will send print(df) to  "text/plain": [...]

df_style = df.style.set_caption("data")
display(df_style)  # this will send print(df_style) to  "text/plain": [...]

Issue Description

Refer to my issue in nbconvert

Basically, nbconvert use what is in "text/plain": [...]. Displaying something using display seems to send object.__repr__ or object.__str__ there. Sadly, pd.style.Styler return <pandas.io.formats.style.Styler at 0x...> on print. Please at least change pd.style.Styler.__repr__ and pd.style.Styler.__str__ into a human readable meaningful text, that is, at least, sending pd.style.Styler.data.__repr__ and pd.style.Styler.data.__str__.

Expected Behavior

pd.style.Styler.__repr__ and pd.style.Styler.__str__ has a human readable and meaningful text, that is, at least, like pd.style.Styler.data.__repr__ and pd.style.Styler.data.__str__.

Installed Versions

I use python 3.8, pd.show_versions throws error.

Here is pandas version: '2.0.3'