¿Cómo imprimir una barra inversa literal para obtener \pm en un marco de datos de pandas para generar barras de error adecuadas en una tabla de latex en python?

Obviamente he visto https://stackoverflow.com/questions/19095796/how-to-print-a-single-backslash y duplicados relacionados https://stackoverflow.com/questions/24278190/cant-print-single-backslash-in-python, https://stackoverflow.com/questions/56689741/how-to-print-a-single-backslash-in-python-in-a-string, https://stackoverflow.com/questions/301068/quoting-backslashes-in-python-string-literals.

Pero creo que mi problema es que tengo pandas involucrado y no está generando la tabla de LaTeX correcta que necesito. Obtengo:

Initialization Test Accuracy
0 Random 0.200+-0.029
1 Random2 0.200+-0.0
\begin{tabular}{ll}
\toprule
Initialization & Test Accuracy \
\midrule
Random & 0.200\textbackslash pm0.029 \
Random2 & 0.200\textbackslash pm0.0 \
\bottomrule
\end{tabular}

Pero necesito:

Initialization Test Accuracy
0 Random 0.200+-0.029
1 Random2 0.200+-0.0
\begin{tabular}{ll}
\toprule
Initialization & Test Accuracy \
\midrule
Random & 0.200 \pm 0.029 \
Random2 & 0.200 \pm 0.0 \
\bottomrule
\end{tabular}

¿cómo puedo hacer que pandas imprima la tabla de LaTeX correcta para mí?

script completo:

import pandas as pd

data = {'firstcolumn':  ['firstvalue', 'second_value', ...],

'secondcolumn': ['firstvalue', 'second_value', ...],

....

}

import pandas as pd

from uutils import putpmtopandasdata

def putpmtopandasdata(data: dict) -> dict:
    """
    Cambiar +- a \pm para su visualización en LaTeX.

ref:
    - https://stackoverflow.com/questions/70008992/how-to-print-a-literal-backslash-to-get-pm-in-a-pandas-data-frame-to-generate-a
"""
for column_name, data_values in data.items():
    # data[column_name] = [data_value.replace('+-', r'\pm') for data_value in data_values]
    data[column_name] = [data_value.replace('+-', r'\\pm') for data_value in data_values]
    # data[column_name] = [data_value.replace('+-', '\pm') for data_value in data_values]
return data


data = {
    'Initialization': ['Random',
                       'Random2',
                       ],

'Test Accuracy': ['0.200+-0.029',
                  '0.200+-0.0',
                  ],


}

df = pd.DataFrame(data)
print(df)
data = putpmtopandasdata(data)
df = pd.DataFrame(data)

print(df.to_latex(index=False))