In 2019.12 or 12.1, Tesla added a new Controls > Software UI, with the following release note:
"You can now view details about your vehicle software by tapping Controls > Software. In addition to your current software version, you can see when there is a new software update package available to be downloaded. A download progress bar is displayed once your car is connected to WiFi. After the download is complete you will continue to be able to schedule when to install the software update or install it immediately."
Since the car and app don't notify you until the update is finished downloading, I'm wondering if anyone has actually seen the download progress bar. Unless you just happen to check Controls > Software when there's an update waiting to download, it's not something you would know to look for. Also, the wording of the release note implies that the update won't be downloaded unless you're connected to WiFi, which isn't supposed to be a requirement for people with premium connectivity (except for map updates). At this point, everyone has premium connectivity except Model 3 owners with the partial premium interior.