I just tested it on my Galaxy A32 5G on Android 12, with Samsung's Clock app. When I set a Timer (i.e., the countdown function), on the lockscreen, I see the Timer notification with the time left (Timer will always show the time left, since it's a countdown).

Go to Settings>Lock Screen, and tap the word Notifications (not the toggle). Make sure Details is selected, and Hide Content is toggled off.