Attaching new lines to existing excel in python with data from multiple csvs

I'm trying to read out data from multiple csv files in a folder, selecting specific column, adding the file name as an additional column and finally writing this to an existing excel.

The print output does what I'd like to do, but I don't seem to get the part working, where the data are attached to the excel sheet.

import requests
import os
import pandas as pd
import time
import xlwt
import glob


files = glob.glob("*.csv") 

writer = pd.ExcelWriter('output.xls', engine='xlsxwriter')
writer.close()

for i in files:
    
    df=pd.read_csv(i, usecols = ['column1', 'column2'])
    df['Filename Column'] = i.split(".")[0]
    df.to_csv(i.split(".")[0]+".csv")
    print(df)
    df_combined = pd.concat([df])
    reader = pd.read_excel(r'output.xls')
    df_combined.to_excel(writer, index=False, startrow=len(reader)+1)

The Excel remains empty, when I do it like that.

This code is what I've come up with.

import glob
import pandas as pd
from typing import List


if __name__ == "__main__":
    final_df: pd.DataFrame = pd.read_excel("dataset.xlsx", engine="openpyxl")

    files: List = glob.glob("*.csv")
    for file in files:
        added_df: pd.DataFrame = pd.read_csv(file, usecols=["column1", "column3"])
        added_df["Filename"] = file.split(".")[0]
        final_df: pd.DataFrame = pd.concat([final_df, added_df])

    final_df.to_excel("dataset.xlsx", index=False)