Excel try to recognize date format even if you cast your column Today as string.
Suppose the following dataframe:
df = pd.DataFrame({'ID': [123, 456, 789], 'Name': ['Louis', 'Paul', 'Alexandre'],
'Today': pd.date_range('2021-12-14', periods=3, freq='D')})
print(df)
# Output:
ID Name Today
0 123 Louis 2021-12-14
1 456 Paul 2021-12-15
2 789 Alexandre 2021-12-16
If you export your dataframe with df.to_excel('data.xlsx', index=False), you got:

Here, the trick:
with pd.ExcelWriter('data.xlsx', engine='openpyxl') as writer:
df.to_excel(writer, index=False)
wb = writer.book
ws = wb.active
# For the third column only (Today, Col C)
for col in ws.iter_cols(min_col=3, max_col=3):
# For all rows below header (C2, C3, C4, ...)
for cell in col[1:]:
cell.number_format = 'DD/MM/YYYY'
Now, you got:
