It is not entirely clear from your post what type of alarm you are referring to. Are you talking about the built-in iOS Alarm Clock in the Clock app, or an alarm provided by a third-party app?
This distinction is important because you describe the alarms as “appearing as minuscule orange dots at the top of the screen.” That description does not correspond to a standard iOS Alarm Clock feature or indicator in iOS 27 or earlier versions of iOS.
The built-in Clock app has established visual indicators for alarms, but tiny orange dots at the top of the screen are not a normal iOS alarm notification or status indicator. If you are seeing such dots, they may be associated with a third-party application, another system indicator, or possibly a particular interface element that is being interpreted as an alarm indicator.
It would therefore be helpful if you could clarify which alarm application you are using and, preferably, provide a screenshot showing the orange dots. That would make it possible to identify exactly what you are referring to and determine whether the behavior is actually related to an alarm.
Without that information, it would be difficult to attribute the orange dots specifically to the iOS Alarm Clock.