I was able to come up with my own answer. The code is below.

Notes:

1. This only applies to number formatting but can easily be modified for any Styler format.
2. pandas display options usually print the minimum number of rows and the maximum number of columns (no option display.min_columns).

I had some help from the thread StackOverflow: Merging Pandas styler object side by side.

from IPython.display import display, HTML

# Function
def style_with_truncation(df, formatter='{:.2f}', min_rows=10, max_columns=20):
    half_rows = min_rows // 2
    half_cols = max_columns // 2

    # Left half
    upper_left = df.iloc[:half_rows ,:half_cols].style.format(formatter=formatter)
    lower_left = df.iloc[-half_rows:,:half_cols].style.format(formatter=formatter)

    ellipsis_half_row_left = pd.DataFrame([['...'] * (half_cols)],
                                          index=['...'], columns=upper_left.data.columns)
    
    left_half = upper_left.concat(ellipsis_half_row_left.style).concat(lower_left)

    # Right half
    upper_right = df.iloc[:half_rows ,-half_cols:].style.format(formatter=formatter)
    lower_right = df.iloc[-half_rows:,-half_cols:].style.format(formatter=formatter)
    
    ellipsis_half_row_right = pd.DataFrame([['...'] * (half_cols)],
                                          index=['...'], columns=upper_right.data.columns)

    right_half = upper_right.concat(ellipsis_half_row_right.style).concat(lower_right)

    # Middle
    ellipsis_column = pd.DataFrame({'...' : ['...'] * (min_rows+1)}, columns=['...'])
    ellipsis_column = ellipsis_column.style
    
    # Set the Styler attribute to be shown side by side
    left_half.set_table_attributes("style='display:inline'")
    right_half.set_table_attributes("style='display:inline'")
    ellipsis_column.set_table_attributes("style='display:inline'")

    # Display the styler objects inline
    row_col_text = f"<p>{df.shape[0]:d} rows × {df.shape[1]:d} columns</p>"
    display(HTML(left_half._repr_html_() +
                 ellipsis_column.hide(axis="index")._repr_html_() +
                 right_half.hide(axis="index")._repr_html_()
                 + row_col_text))

# Example of a function call
min_rows = pd.options.display.min_rows
max_columns = pd.options.display.max_columns
style_with_truncation(df, formatter='{:.2f}', min_rows=min_rows, max_columns=max_columns)

Output: Successful truncation of a stylized DataFrame