Is it possible to count time with Siri?
This just worked for me on my iPhone 11 with current iOS.


Hold side button to invoke Siri
Say, "start timer for 15 seconds."
Timer starts immediatly counting down.


You have to be a little clever to work around the limitations of the voice interface. After all we are not at the point of the computers on Star Trek. Yet.

So for your particular use case, perhaps a command like, "Siri, start timer for an hour." and a bit later you can do something like, "Siri, stop timer."

It requires you to think like how would you tell Siri to do something that you could also do on the phone through a series of taps. And often it will take a few tries to get the phrasing correct, but once you get the hang of it you will learn how to ask a question of Siri that will give you the answer you need in as few words as possible. Kind of like programming the phone with voice.