If not using VoiceOver, it is possible to dismiss an activity from the Dynamic island by swiping left or right across the Dynamic Island. This does not close any related background activity. For example, if you are playing audio and you dismiss the audio waveform and artwork in the Dynamic Island, the music will continue to play in the background. The same goes for when you dismiss a timer – it will still count down in the background even though it is no longer visible on the screen.
There is currently no means of accessing this functionality when VoiceOver is enabled. The ‘dismiss’ gesture does not work and there is no alternative path such as an option in the VoiceOver rotor.
MacRumors has an article on how to dismiss Dynamic Island content: https://www.macrumors.com/how-to/iphone-14-pro-disable-dynamic-island/