> telling the user that your computer will remember your e-mail address in an application completely under your control that will never send it anywhere else on

> telling the user that your computer will remember your e-mail address in an application completely under your control that will never send it anywhere else on its own, just so that you wouldn't have to re-type it every time, is not something that GDPR forces you to do That's exactly what the GDPR enforces. You give the app personally identifying data, so the app needs to disclose what it does with the data because storing it on the computer and not sending it anywhere is still data processing. In this case the data privacy statement needs to tell the user that the data is stored but not shared. If you're not doing anything with the data, then don't ask for it.