If it's large enough, wouldn't cosmic inflation eventually remove the extremities from each other's light cones?

That's true, but once something is outside of your light cone it does not matter what it does, it may as well not even exist to you.

Yeah, they can't accomplish much as adversaries. Except maybe make you worry that they're out there somewhere being better than you. And you can never prove otherwise.

I meant in the time it would take to synchronize/align

Does time matter to a functionally immortal machine?

They could have a super slow clock speed to account for distance and anything truly outside of their light cone might as well not exist.

If you have trillions of years does it matter if a thought takes a million years or so?

This is really key: humans think about everything in finite, human lifetimes. We have no backups, archives nothing - when we die knowledge and experience vanishes.

This wouldn't be true for an AI. Death would be optional.