Yeah interesting ideas.
I think personally, for the space stage, what we should do first is probably something like stellaris etc where all the species hit the space stage at the same time. The galaxy is young and no one has an empire yet and everyone starts spreading out and there is a race for domination, classic 4x style. That would be a good foundation.
However I think later we should add the possibility of evolving when the galaxy is old. So it would be a bit more like Crusader Kings 2 and you get a warp drive only to discover you are surrounded by a massive, autocratic, star empire. What do you do? Swear loyalty? Try to quickly make alliances to secure your position? Convert the their religion? I think it could make for an interesting situation.
Moreover there could be a lot of old technology scattered around that has been forgotten. So yeah you could discover Dyson spheres which just power giant computer simulations, or planet sized creatures, or giant space stations lying abandoned (like the citadel in Mass Effect) or ring worlds and things like that. We can basically trot out all the classic sci fi tropes.
My advice, don’t wake the replicators!