I think the most common view within EA is that future people and matter the same amount as current people, conditional on actually existing. So if you think there is a 50% chance the world will be destroyed by 2200, then you would discount lives in 2200 by 50%.
I definitely agree with your second paragraph, however, and people who value current lives more than future lives will often come to different philosophical conclusions. It's interesting, however, that this frequently doesn't cash out into different beliefs about what we should do today. For example, I think the value of work on pandemic prevention or AI alignment does not depend on multiplying by zillions of potential future people: they're worth doing even just for people alive today.
Ex: https://forum.effectivealtruism.org/posts/KDjEogAqWNTdddF9g/... :
Let me rephrase this in a deliberately inflammatory way: if you're under ~50, unaligned AI might kill you and everyone you know. Not your great-great-(...)-great-grandchildren in the year 30,000 AD. Not even your children. You and everyone you know. As a pitch to get people to care about something, this is a pretty strong one.
But right now, a lot of EA discussion about this goes through an argument that starts with "did you know you might want to assign your descendants in the year 30,000 AD exactly equal moral value to yourself? Did you know that maybe you should care about their problems exactly as much as you care about global warming and other problems happening today?"