df = {'col1': ['1', 'None'], 'col2': ['None', '123']}

df = {'col1': [1, NaN], 'col2': [NaN, 123]}

print(df.replace('None', np.nan).astype(float))

col1   col2
0   1.0    NaN
1   NaN  123.0

df = pd.DataFrame(df)

d = {'col1': ['1', 'None'], 'col2': ['None', '123']}
res = pd.DataFrame({
    k: pd.to_numeric(v, errors='coerce') for k, v in d.items()}, dtype='Int32')
res

   col1  col2
0     1   NaN
1   NaN   123

res.to_dict()
# {'col1': [1, nan], 'col2': [nan, 123]}

res = pd.DataFrame({
    k: pd.to_numeric(v, errors='coerce') for k, v in d.items()}, dtype=object)
res

  col1 col2
0    1  NaN
1  NaN  123

res.to_dict()
#  {'col1': [1.0, nan], 'col2': [nan, 123.0]}

import pandas as pd
d = {'col1': ['1', 'None'], 'col2': ['None', '123']}
df = pd.DataFrame.from_dict(d).replace("None", value=pd.np.nan).astype(float)

col1   col2
0   1.0    NaN
1   NaN  123.0

col1    1 non-null float64
col2    1 non-null float64
dtypes: float64(2)