If they installed a keyboard with the same app id (e.g. com.google.[...]) F-Droid would try to update it and ask the user to confirm the update since F-Droid can't update an app that was installed by another app store.
I'd be curious which keyboard this is. Maybe Gboard took over the app id of the previously foss android keyboard.
PS: I recommend F-Droid Basic which supports silent background updates on any Android 12 without root.
The app it wanted to install was its AOSP, it's likely that I was using another AOSP build at the time but I'm not sure. I've used either AOSP or gboard almost all of the time, so it's 99% likely to have been one of those two.
I'd be curious which keyboard this is. Maybe Gboard took over the app id of the previously foss android keyboard.
PS: I recommend F-Droid Basic which supports silent background updates on any Android 12 without root.