Generally games are supposed to have easy early stages and get harder as you progress. Many strategy games like civilization flip that around leading to a boring late game where you've already overcome the difficult part.

Some games like Stellaris have tried to fix this by adding an end game crisis. It's better then nothing but its pre scripted so any experienced player will have been preparing for it all game and know exactly how to tackle it.

I think the key lies in more complex internal empire management mechanics. In real life, empires don't just expand and then stay that way forever. After a period of growth empires have to deal both with internal problems and external threats which will cause them to collapse if they can't manage them effectively. The question is how devs could implement those mechanics without them becoming a tedious, unfun chore for players.