If you're sending hundred of thousand of emails each months, extracting the logs won't be an easy task, it has to be done from command line most likely, so what you need is to create a console command in mailwizz, just like the one for send-campaigns for example, and make that export the data you want. Most likely you will need a dev to help you export write that command.
From our side, we consider this to be very specific, so i don't add it to the app.
You can explain us in details what you need it to export and what, and if it's simple enough, we can write the code for you, but only if it's simple, otherwise, please get a dev on board.