It seems there are two layers involved here as far as I can see in my Debian 14 system: firstly, the underlying apt update service, and secondly, packagekit update service used by Plasma Discover.
I don’t even know if they work synchronously, but it seems they don’t as sometimes I see updates when I launch Synaptic Package Manager of which Plasma Discover seems not yet aware.
So, it seems there’s some work need to be done here, and it doesn’t seem too complex to let users manage timing software updates in System Settings.
Personally I’ve made some progress in trying to create a more user-friendly method (e.g. opting for offline updates only when system software packages are involved, and opting for online updates in the background otherwise, having a quick view of the full list of pending updates without launching Discover, Synaptic Package Manager etc.), but it seems I just need to spend a little more effort to customize those systemd service and timer config files so that they check updates only when I want exactly.