whether or not (say) that coffee you just drank took you out of the fasted state

A cup of coffee has zero carbohydrates, trace lipids, and about half a gram of protein. That's not going to pull anyone out of a fasting state.

Now, if you're talking about a cup of flavoured milk, that's a different question...

I think I drink coffee but I really drink lattes…

Adding any amount of milk to a coffee adds carbs. And a large number of people add _some_ amount of milk.