I hope I've understood your question right. To find similarity score you can use difflib built-in module:
from difflib import SequenceMatcher
def similar(a, b):
    return SequenceMatcher(None, a, b).ratio()
for s1 in df['A header']:
    df[s1] = [similar(s1, s2) for s2 in df['A header']]
print(df)
Prints:
                A header  schwabstsoct2022  schwabsts  schwabregionaloct2022  schwabregional2  flagstar-2022  flagstar-2021
0       schwabstsoct2022          1.000000   0.720000               0.702703         0.516129       0.482759       0.413793
1              schwabsts          0.720000   1.000000               0.466667         0.500000       0.272727       0.272727
2  schwabregionaloct2022          0.702703   0.466667               1.000000         0.833333       0.352941       0.294118
3        schwabregional2          0.516129   0.500000               0.833333         1.000000       0.142857       0.142857
4          flagstar-2022          0.482759   0.272727               0.411765         0.285714       1.000000       0.923077
5          flagstar-2021          0.413793   0.272727               0.352941         0.285714       0.923077       1.000000