Following up on my entry in this bug report:
Removing $HOME/.config/PlasmaDiscoverUpdates and restarting DiscoverNotifier fixed the issue only once.
Today I did not have any notification about updates being available, I performed a manual update using apt, and still did not receive a notification from Discover, then I removed the config file and restarted DiscoverNotifier once more. That did then give me a notification about updates pending.
The notifier is definitely broken in Trixie with no good workaround.