The one-tap operations share feature uses the default share app. In order to change the default share app, you should connect with a device, go to the download data screen (do not use ‘Play’ this one time), download some data and then select the “share” button on the bottom (the one that is shaped like a less than sign with a solid circle at each corner).
Use your new gmail app & email to share the data. Once the data is shared the app used will become the default share app. The next time you execute the one-tap operations it will use the newly selected default app (gmail now). If the gmail app is not using your gmail email address then you will need to change that in the gmail app settings.