BUG: Modify an existing xlsx file with PANDAS and MIME TYPE ERROR

[macifTest]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

The code bellow :

data_filtered = pd.DataFrame(
        [date, date, date, date], 
        index=[2,3,4,5]
    )

    book = openpyxl.load_workbook(file_origin)

    with pd.ExcelWriter(
        file_modif,
        engine="openpyxl",
        #mode="a",        
        datetime_format='dd/mm/yyyy hh:mm:ss', 
        date_format='dd/mm/yyyy'
        #if_sheet_exists="overlay"

    ) as writer:
        writer.book = book
        writer.sheets = dict((ws.title, ws) for ws in book.worksheets)       
        data_filtered.to_excel(writer, sheet_name="PCA pour intégration", index=False, startrow=2, startcol=5, header=False, verbose=True)

Issue Description

I have an issue with the use of Pandas + ExcelWriter + load_workbook.
My need is to be able to modify data from an existing excel file (without deleting the rest).
It works partly, but when I check the MIME Type of the produced file and the MIME TYPE of the original one, it is different.
The application under test use the same MIME TYPE verification as the website https://www.htmlstrip.com/mime-file-type-checker

Original : application/vnd.openxmlformats-officedocument.spreadsheetml.sheet
Modify : application/octet-stream

Expected Behavior

The code bellow :

data_filtered = pd.DataFrame(
[date, date, date, date],
index=[2,3,4,5]
)

book = openpyxl.load_workbook(file_origin)

with pd.ExcelWriter(
    file_modif,
    engine="openpyxl",
    #mode="a",        
    datetime_format='dd/mm/yyyy hh:mm:ss', 
    date_format='dd/mm/yyyy'
    #if_sheet_exists="overlay"

) as writer:
    writer.book = book
    writer.sheets = dict((ws.title, ws) for ws in book.worksheets)       
    data_filtered.to_excel(writer, sheet_name="PCA pour intégration", index=False, startrow=2, startcol=5, header=False, verbose=True)  

Installed Versions

INSTALLED VERSIONS

commit : bb1f651
python : 3.8.10.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.18363
machine : AMD64
processor : Intel64 Family 6 Model 85 Stepping 7, GenuineIntel
byteorder : little
LC_ALL : None
LANG : fr_FR.UTF-8
LOCALE : fr_FR.cp1252

pandas : 1.4.0
numpy : 1.22.1
pytz : 2021.1
dateutil : 2.8.2
pip : 21.2.4
setuptools : 58.0.2
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : 3.0.2
lxml.etree : 4.7.1
html5lib : None
pymysql : None
psycopg2 : 2.8.6
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : 4.10.0
bottleneck : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : 2.0.1
xlwt : 1.3.0
zstandard : None

[twoertwein]

None of the attributes of ExcelWriter are considered public (this will change in 1.5 #45572).

I don't recommend overwriting .book but I assume that something similar as described here might work for you.

[macifTest]

Thanks for your reply.
I tried your suggestion, but it doesn't work. The MIME type is still not good.
This shows me: application/zip
bellow the code I used :
with open(file_origin, mode="rb+") as handle:
book = openpyxl.load_workbook(handle)
handle.seek(0)
with pd.ExcelWriter(
handle,
if_sheet_exists="overlay",
engine="openpyxl",
mode="a"
) as xl_writer:
xl_writer.book = book # still uses the same handle!
xl_writer.sheets = dict((ws.title, ws) for ws in book.worksheets)
chunk = pd.DataFrame([date, date, date, date], index=[2,3,4,5])
chunk.to_excel(xl_writer, merge_cells=False, index=False, startrow=2, startcol=5, header=False, verbose=True, sheet_name="PCA pour intégration")

Thanks