This asked, understandably, for storage permission. This prompted me to give access to the sdcard, however, I had the option to select a single folder (or actually directly creating it within the prompt) that the app will have access to. I.e. Signal now has access to sdcard/signalbackups/ but not to the whole sdcard. (unless this whole new permission process wasn't Android but the Signal app. I rarely download apps and have to give storage permissions).

This used to be different, but times of giving access to full internal or external sdcards are over. Unfortunately though, the UX isn't perfect. I felt like I needed to know that I only want to give it access to a part of the sdcard and actively look that this is indeed possible. But that might be my bias from previous usage talking.