If you want to update all your F-Droid apps at once on a non-rooted Android, you need to go through all of them one by one. Basically: click upgrade, click "Install", wait for Android to do its stuff, do the same for the next app. It is extremely impractical and most of the apps I installed from F-Droid are severely out of date because of this Android restriction.
Fortunately F-Droid has an "Upgrade all" button which will download all the APKs in the background, but the click&wait loop sequence cannot be avoided.
Not that this is perfect either but if you know how to grab the APKs and developer mode is enabled, you can script the installs using adb from a computer. I agree there is room for improvement to help make this process more seamless, but it still much more flexible than what is being offered by Apple.