In practice, it should make no difference. That's already much, much further than any of us can comprehend. It's a hundred times the length of recorded human history. What would it really matter?
On the other hand, it would seem so short, I think a sense of nihilism would already take hold.
Even with the Big Freeze or Big Crunch of the universe, there’s at least some hope that some currently unknown science, energy source, etc. might be accessible to us in 1M years that could delay or reduce the severity of the event.
But, let’s say there’s a an event that will somehow destroy our entire solar system in 500 years, that would certainly divide people into two camps: one hell bent on escaping the solar system at all costs and another determined to enjoy every last moment before extinction.
There's at least one or two issues that we maybe should think about addressing before it's too late.
I see what you mean by setting a hard stop, it does mean little in the end. The Wikipedia timeline, which makes a lot of assumptions, show galaxy formation stopping at 100 trillion years from now.
https://en.wikipedia.org/wiki/Timeline_of_the_far_future
We're human beings who only came on the scene around 200,000 years ago. It's impressive that we can work out the math and physics to try to comprehend 100 trillion years, but it is impossible to even imagine where conscious life would be at that point, if it exists at all.