The API that FDroid is using has only just come out. Before then, without using root and scripts to enable higher privileges, no app could auto-update in the background.
FDroid has long has the ability to automatically download updates, however installation always required a confirmation from the user for each app.
The API that FDroid is using has only just come out.
Not true. Android has supported rootless unattended upgrades at a system level since Android 12 (October 4 2021). That was nearly 2 and a half years ago, so it's been a while.
This is what Neo Store used. F-Droid only just now got around to supporting this with this recent update.
According to the article, F-droid is using a library that isn't the latest, because it doesn't support "gentle updates" (updates that are heuristically scheduled to stay out of the way of the user).